Probability and Conditional Probability

The correct answer is \(3 tenths\). It’s given that there are a total of \(100\) tiles of equal area, which is the total number of possible outcomes. According to the table, there are a total of \(30\) red tiles. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. By definition, the probability of selecting a red tile is given by \(30/100\), or \(3 tenths\). Note that 3/10 and .3 are examples of ways to enter a correct answer.

Choice B is correct. According to the table, a total of 671 customers asked about a bill. Of these, 48 also asked for repairs. Therefore, if a customer who asked about a bill is selected at random, the probability that the customer also asked for repairs is .Choice A is incorrect. This is the probability that a customer selected at random from all customers who called on Monday both asked for repairs and asked about a bill. Choice C is incorrect. This is the probability that a customer selected at random from all customers who called on Monday asked for repairs, regardless of whether or not the customer asked about a bill. Choice D is incorrect. This is the probability that a customer selected at random from those who asked for repairs also asked about a bill.

Choice B is correct. In total, there are 6 people in the Human Resources department. Of those 6, 2 have a master’s ° as their highest level of education. Therefore, the probability of an employee selected at random from the Human Resources department having a master’s ° is, which simplifies to .Choice A is incorrect; it is the probability that an employee selected at random from either department will be in the Human Resources department and have a master’s °. Choice C is incorrect; it is the probability that an employee with a master’s ° selected at random will be in the Human Resources department. Choice D is incorrect; it is the probability that an employee selected at random from either department will have a master’s °.

The correct answer is \(13/50\). It's given that a box contains \(13\) red pens and \(37\) blue pens. If one of these pens is selected at random, the probability of selecting a red pen is the number of red pens in the box divided by the number of red and blue pens in the box. The number of red and blue pens in the box is \(13 + 37\), or \(50\). Since there are \(13\) red pens in the box, it follows that the probability of selecting a red pen is \(13/50\). Note that 13/50 and .26 are examples of ways to enter a correct answer.

Choice B is correct. It’s given that there are \(20\) buttons in a bag and \(8\) of the buttons are white. If one button from the bag is selected at random, the probability of selecting a white button is the number of white buttons in the bag divided by the total number of buttons in the bag. Therefore, if one button from the bag is selected at random, the probability of selecting a white button is \(8 twentieths\). Choice A is incorrect. This is the probability of selecting an orange button from the bag. Choice C is incorrect. This is the probability of selecting a brown button from the bag. Choice D is incorrect. This is the probability of selecting a button that isn't white from the bag.

Choice B is correct. If a number from the data set is selected at random, the probability of selecting a -number is the count of -numbers in the data set divided by the total count of numbers in the data set. It's given that a data set of three numbers is shown. It follows that the total count of numbers in the data set is \(3\). In the data set shown, \(-13\) is the only -number. It follows that the count of -numbers in the data set is \(1\). Therefore, if a number from the data set is selected at random, the probability of selecting a -number is \(1 third\). Choice A is incorrect. This is the probability of selecting a -number from a data set that doesn’t contain any -numbers. Choice C is incorrect. This is the probability of selecting a positive number, not a -number, from the data set. Choice D is incorrect. This is the probability of selecting a -number from a data set that contains only -numbers.

Choice A is correct. It is given that there are 180 female penguins in the exhibit. Therefore, of the female penguins is penguins. According to the table, there are 59 female chinstrap penguins, 27 female emperor penguins, 54 female gentoo penguins, and 40 female macaroni penguins. So the female chinstrap penguin population is the closest to 60, or of the total female population in the exhibit.Choices B, C, and D are incorrect and may result from reading data from the table incorrectly. Since the total female penguin population is 180, of the total female penguin population is 60. The numbers of female emperor (27), female gentoo (54), and female macaroni (40) penguins are not as close to 60 as the number of female chinstrap penguins (59).

Choice B is correct. If a house from the street is selected at random, the probability of selecting a house that is blue is equal to the number of houses on the street that are blue divided by the total number of houses on the street. Since there are \(2\) blue houses on a street with \(7\) total houses, the probability of selecting a house that is blue from this street is \(2 sevenths\). Choice A is incorrect. This is the probability of selecting a house that is blue from a street on which \(1\) of the \(7\) houses is blue. Choice C is incorrect. This is the probability of selecting a house that is not blue from this street. Choice D is incorrect. This is the probability of selecting a house that is blue from a street on which all the houses are blue.

Choice A is correct. Multiplying the number of marbles in the bag by the probability of selecting a blue marble gives the number of blue marbles in the bag. Since the bag contains a total of 60 marbles and the probability that a blue marble will be selected from the bag is 0.35, there are a total of blue marbles in the bag.Choice B is incorrect and may result from subtracting 35 from 60. Choice C is incorrect. This would be the number of blue marbles in the bag if there were a total of 100 marbles, not 60 marbles. Choice D is incorrect. This is the number of marbles in the bag that aren’t blue.

Choice C is correct. It’s given that \(29\) out of every \(100\) beads that the machine produces have a defect. It follows that if the machine produces \(k\) beads, then the number of beads that have a defect is \(29/100 k\), for some constant \(k\). If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, \(29/100 k\), divided by the number of beads produced by the machine, \(k\). Therefore, the probability of selecting a bead that has a defect is \(\29/100 k/k\), or \(29/100\). Choice A is incorrect and may result from conceptual or computational errors. Choice B is incorrect and may result from conceptual or computational errors. Choice D is incorrect and may result from conceptual or computational errors.

Choice B is correct. The probability of selecting a positive number is the number of positive numbers in the data set divided by the total number of numbers in the data set. There is \(1\) positive number in this data set. There are \(3\) total numbers in this data set. Thus, if a number from this data set is selected at random, the probability of selecting a positive number is \(1 third\). Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This is the probability of selecting a -number from this data set. Choice D is incorrect and may result from conceptual or calculation errors.

Choice C is correct. The sum of the number of states with a state-level sales tax is . Of these states, 6 don’t have a state-level income tax. Therefore,, or about 13.3%, of states with a state-level sales tax don’t have a state-level income tax. Choice A is incorrect. This is the number of states that have a state-level sales tax and no state-level income tax. Choice B is incorrect. This is the percent of states that have a state-level sales tax and no state-level income tax. Choice D is incorrect. This is the percent of states that have no state-level income tax.

Choice B is correct. The sample space is restricted to the presidents who were at least 50 years old when they first took office. Therefore, the sum of the values in the final four rows of the table,, is the total number of presidents in the sample space. The number of presidents who were at least 60 years old is the sum of the values in the final two rows of the table: . Thus, the fraction of the 34 presidents who were at least 50 years old when they first took office who were at least 60 years old is .Choice A is incorrect. This is the fraction of all presidents in the table who were at least 60 years old when they first took office. Choice C is incorrect and may result from treating the number of presidents who were between 50 and 59 years old when they first took office, instead of the number of presidents who were at least 50 years old, as the sample space. Choice D is incorrect and may result from a calculation error.

Choice A is correct. If one of the gemstones is selected at random, the probability of selecting a gemstone of color Y is equal to the number of gemstones of color Y divided by the total number of gemstones. According to the table, there are \(3\) gemstones of color Y, and it's given that the total number of gemstones is \(157\). Therefore, if one of the gemstones is selected at random, the probability of selecting a gemstone of color Y is \(3/157\). Choice B is incorrect. This is the probability of selecting a gemstone of color Z. Choice C is incorrect. This is the probability of selecting a gemstone of color X. Choice D is incorrect. This is the probability of selecting a gemstone that's not of color Y.

Choice B is correct. If 1,200 customers register for new accounts every day, then (1,200)(5) = 6,000 customers registered for new accounts in the first 5 days. Therefore, of the first 60,000 new accounts that were registered,, or, were registered in the first 5 days.Choice A is incorrect. The fraction represents the fraction of accounts registered in 1 of the first 5 days. Choice C is incorrect and may result from conceptual or computation errors. Choice D is incorrect. The fraction represents the fraction of the first 60,000 accounts that were registered in 1 day.

Choice B is correct. Since there are n nonfiction and 12 fiction books on the bookshelf, represents the total number of books. If one of these books is selected at random, the probability of selecting a nonfiction book is equivalent to the number of nonfiction books divided by the total number of books. Therefore, the probability of selecting a nonfiction book, in terms of n, is .Choice A is incorrect. This expression represents the number of nonfiction books divided by the number of fiction books. Choice C is incorrect. This expression represents the number of fiction books divided by the number of nonfiction books. Choice D is incorrect. This expression represents the probability of selecting a fiction book.

The correct answer is \(88\). It's given that there are a total of \(275\) attendees and each attendee is assigned to either group A, group B, or group C. It's also given that if one of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is \(0.44\) and the probability of selecting an attendee who is assigned to group B is \(0.24\). It follows that there are \(0.44(275)\), or \(121\), attendees who are assigned to group A and \(0.24(275)\), or \(66\), attendees who are assigned to group B. The number of attendees who are assigned to group C is the number of attendees who are not assigned to group A or group B. In other words, the number of attendees who are assigned to group C is the total number of attendees minus the number of attendees who are assigned to group A and group B. Therefore, the number of attendees who are assigned to group C is \(275 -121 -66\), or \(88\).

The correct answer is \(23/60\). It's given that one of the participants will be selected at random. The probability of selecting a participant from group A given that the participant is at least \(10\) years of age is the number of participants in group A who are at least \(10\) years of age divided by the total number of participants who are at least \(10\) years of age. The table shows that in group A, there are \(14\) participants who are \(10\)–\(19\) years of age and \(9\) participants who are \(20 +\) years of age. Therefore, there are \(14 + 9\), or \(23\), participants in group A who are at least \(10\) years of age. The table also shows that there are a total of \(30\) participants who are \(10\)–\(19\) years of age and \(30\) participants who are \(20 +\) years of age. Therefore, there are a total of \(30 + 30\), or \(60\), participants who are at least \(10\) years of age. It follows that the probability of selecting a participant from group A given that the participant is at least \(10\) years of age is \(23/60\). Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.

Choice B is correct. There were 64 days with no rain. It was a weekend day for 16 of those 64 days. So 16 out of 64 of the days with no rain were weekend days. Because the day is selected at random, each day has an equal chance of being selected, so the probability is . Choice A is incorrect. It is the probability that a day selected at random from any one of the days during the 12 weeks is a weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekend days has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is a weekday.

Choice A is correct. The probability of randomly selecting a defective MP3 player from the shipment is equal to the number of defective MP3 players divided by the total number of MP3 players in the shipment. Therefore, the probability is, which is equivalent to 0.004.Choice B is incorrect because 0.04 represents 4 defective MP3 players out of 100 rather than out of 1,000. Choice C is incorrect because 0.4 represents 4 defective MP3 players out of 10 rather than out of 1,000. Choice D is incorrect. This is the number of defective MP3 players in the shipment.

The correct answer is 42. It’s given that in Nigeria on September 30, 2015, the probability of selecting an MTN subscriber from all Internet subscribers is 0.43, that there were p million, or, MTN subscribers, and that there were 97 million, or 97,000,000, Internet subscribers. The probability of selecting an MTN subscriber from all Internet subscribers can be found by dividing the number of MTN subscribers by the total number of Internet subscribers. Therefore, the equation can be used to solve for p. Dividing 1,000,000 from the numerator and denominator of the expression on the left-hand side yields . Multiplying both sides of this equation by 97 yields, which, to the nearest integer, is 42.

The correct answer is . It’s given that the number of email responses is twice the number of phone responses. Therefore, if the number of phone responses is p, then the number of email responses is . The table shows that 20% of people who responded by phone preferred aπcnic. It follows that the expression represents the number of these people. The table also shows that 5% of the people who responded by email preferred aπcnic. The expression, or, represents the number of these people. Therefore, a total of, or people preferred aπcnic. Thus, the probability of selecting at random a person who responded by email from the people who preferred aπcnic is, or . Note that 1/3, .3333, and 0.333 are examples of ways to enter a correct answer.

Choice B is correct. The probability of an event occurring is the ratio of the number of favorable outcomes to the total number of possible outcomes. It’s given that there are \(45\) band members, which is the total number of possible outcomes. It's also given that there are \(11\) band members who play saxophone. Therefore, the number of favorable outcomes is \(11\). Thus, the probability of selecting a band member who plays saxophone is \(11/45\). Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This is the probability of selecting a band member who does not play saxophone. Choice D is incorrect and may result from conceptual or calculation errors.

Choice B is correct. If one of the teens surveyed is selected at random, the probability that the teen talks on a cell phone daily is equal to the quotient of the total number of teens who reported that they talk on a cell phone daily, 415, and the total number of teens surveyed, 799. Therefore, this probability is equal to .Choice A is incorrect. This fraction represents the probability of selecting at random any one of the 799 teens surveyed. Choice C is incorrect and may result from conceptual errors. Choice D is incorrect. This fraction represents the probability of selecting at random one of the 799 teens surveyed who doesn’t talk on a cell phone daily.

The correct answer is \(1 fourteenth\). If one vertex of the polygon is selected at random, the probability that the letter \(D\) will be at the selected vertex is equal to the number of vertices labeled with the letter \(D\) divided by the total number of vertices. It's given that each vertex is labeled with one of the \(14\) letters \(A\) through \( N\), with a different letter at each vertex. It follows that there is \(1\) vertex labeled with the letter \(D\). It's also given that the polygon is \(14\)-sided. It follows that there are a total of \(14\) vertices. Thus, the probability that the letter \(D\) will be at the selected vertex is \(1 fourteenth\). Note that 1/14, .0714, and 0.071 are examples of ways to enter a correct answer.

Choice D is correct. If a member of the organization is selected at random, the probability that the selected member is at least \(40\) years old is equal to the number of members who are at least \(40\) years old divided by the total number of members. According to the table, there are a total of \(135\) members of the organization, and \(107\) of these members are at least \(40\) years old. Therefore, the probability that the selected member is at least \(40\) years old is \(107/135\). Choice A is incorrect. This is the probability that the selected member is less than \(40\) years old. Choice B is incorrect. This is the probability that the selected member lives east of the river. Choice C is incorrect. This is the probability that the selected member lives west of the river.

Choice D is correct. It’s given that at a movie theater, there are a total of \(350\) customers and that each customer is located in either theater A, theater B, or theater C. If the probability of selecting a customer in theater A is \(0.48\), then \((0.48)(350)\), or \(168\), customers are located in theater A. If the probability of selecting a customer in theater B is \(0.24\), then \((0.24)(350)\), or \(84\), customers are located in theater B. It follows that there are \(168 + 84\), or \(252\), customers in theater A and theater B. Therefore, there are \(350 -252\), or \(98\), customers in theater C. Choice A is incorrect. This is the percent, not the number, of the customers that are located in theater C. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This is the number of customers that are located in theater B, not theater C.

Choice C is correct. If one of these planets is selected at random, the probability that the selected planet will be rocky is calculated by dividing the number of planets that are considered rocky by the total number of planets. It’s given that 4 of the 8 total planets are considered rocky. Therefore, the probability that the selected planet will be rocky is, which is equivalent to .Choices A and B are incorrect. These represent the probability if 1 of the 8 planets was considered rocky (choice A) and if 2 of the 8 planets were considered rocky (choice B). Choice D is incorrect and may result from dividing the total number of planets by the number of planets that are considered rocky.

Choice D is correct. If one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is equal to the number of igneous rocks in the collection divided by the total number of rocks in the collection. According to the table, there are \(10\) igneous rocks in the collection, and it's given that there's a total of \(70\) rocks in the collection. Therefore, if one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is \(10/70\). Choice A is incorrect. This is the number of igneous rocks in the collection divided by the number of sedimentary rocks in the collection, not divided by the total number of rocks in the collection. Choice B is incorrect. This is the number of igneous rocks in the collection divided by the number of metamorphic rocks in the collection, not divided by the total number of rocks in the collection. Choice C is incorrect. This is the number of igneous rocks in the collection divided by the number of rocks in the collection that aren't igneous, not divided by the total number of rocks in the collection.

Choice C is correct. If a tree from one of these rows is selected at random, the probability of selecting a maple tree, given that the tree is \(20\) feet or taller, is equal to the number of maple trees that are \(20\) feet or taller divided by the total number of trees that are \(20\) feet or taller. It's given that there are \(6\) rows of birch trees, and each row of birch trees has \(8\) trees that are \(20\) feet or taller. This means that there are a total of \(6(8)\), or \(48\), birch trees that are \(20\) feet or taller. It's given that there are \(5\) rows of maple trees, and each row of maple trees has \(9\) trees that are \(20\) feet or taller. This means that there are a total of \(5(9)\), or \(45\), maple trees that are \(20\) feet or taller. It follows that there are a total of \(48 + 45\), or \(93\), trees that are \(20\) feet or taller. Therefore, the probability of selecting a maple tree, given that the tree is \(20\) feet or taller, is \(45/93\), or \(15/31\). Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Choice C is correct. If one of these students is selected at random, the probability of selecting a student whose vote for the new mascot was for a lion is given by the number of votes for a lion divided by the total number of votes. The given table indicates that the number of votes for a lion is \(20\) votes, and the total number of votes is \(80\) votes. The table gives the distribution of votes for \(80\) students, and the table shows a total of 80 votes were counted. It follows that each of the \(80\) students voted exactly once. Thus, the probability of selecting a student whose vote for the new mascot was for a lion is \(20/80\), or \(1 fourth\). Choice A is incorrect and may result from conceptual or computational errors. Choice B is incorrect and may result from conceptual or computational errors. Choice D is incorrect and may result from conceptual or computational errors.

Choice D is correct. It’s given that there are \(7\) red, \(4\) white, \(33\) blue, and \(33\) yellow cubes in the bag. Therefore, there are a total of \(7 + 4 + 33 + 33\), or \(77\), cubes in the bag. If the cube is neither blue nor yellow, then it must be either red or white. Therefore, the probability of selecting a cube that is neither blue nor yellow is equivalent to the probability of selecting a cube that is either red or white. If one of these cubes is selected at random, the probability of selecting a cube that is either red or white is equal to the sum of the number of red cubes and white cubes divided by the total number of cubes in the bag. There are \(7\) red cubes, \(4\) white cubes, and \(77\) total cubes in the bag. Therefore, the probability of selecting a red or white cube is \(7 + 4/77\), which is equivalent to \(11/77\), or \(1 seventh\). Thus, if one cube is selected at random, the probability of selecting a cube that is neither blue nor yellow is \(1 seventh\). Choice A is incorrect. This is the probability of selecting a cube that is either blue or yellow, rather than the probability of selecting a cube that is neither blue nor yellow. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Choice A is correct. The total number of state parks in the state is . According to the table, 5 of these have camπng facilities but not bicycle paths. Therefore, if a state park is selected at random, the probability that it has camπng facilities but not bicycle paths is .Choice B is incorrect. This is the probability that a state park selected at random from the state parks with camπng facilities does not have bicycle paths. Choice C is incorrect. This is the probability that a state park selected at random from the state parks with bicycle paths does not have camπng facilities. Choice D is incorrect. This is the probability that a state park selected at random from the state parks without bicycle paths does have camπng facilities.

The correct answer is 8. In this group, of the people who are rhesus -have blood type B. The total number of people who are rhesus -in the group is, and there are 2 people who are rhesus -with blood type B. Therefore, . Combining like terms on the left-hand side of the equation yields . Multiplying both sides of this equation by 9 yields, and multiplying both sides of this equation by yields . Subtracting 10 from both sides of this equation yields .

Choice B is correct. The table summarizes all 1,000 responses from the students surveyed. If 312 are males who play a sport, 220 are females who play a sport, and 216 are females who do not play a sport, then 1,000 – 312 – 220 – 216 = 252 males who do not play a sport.Choices A, C, and D are incorrect. If 109 males who do not play a sport responded, then the table summary would be 109 + 312 + 220 + 216 = 857 total student responses rather than 1,000. If 468 males who do not play a sport responded, then the table summary would be 468 + 312 + 220 + 216 = 1,216 total student responses rather than 1,000. If 688 males who do not play a sport responded, then the table summary would be 688 + 312 + 220 + 216 = 1,436 total student responses rather than 1,000.

Choice B is correct. This probability is calculated by dividing the number of baritone singers by the total number of men registered for singing lessons. It’s given that a total of 25 men registered for singing lessons and that there are 10 baritones. Therefore, the probability of selecting a baritone from this group at random is, which is equivalent to 0.40.Choice A is incorrect. This would be the probability of selecting a baritone at random if there were 100 total men who registered for singing lessons. Choice C is incorrect. This is the probability of selecting a singer at random who isn’t a baritone. Choice D is incorrect. This would be the probability of selecting a baritone at random if there were 15 total men registered for singing lessons.

Choice B is correct. According to the table, 140 students from the two high schools completed summer internships in 2010. Of these, 65 were from Valley High School. Therefore, of the students who completed summer internships in 2010, represents the fraction who were from Valley High School.Choice A is incorrect. This is the difference between the numbers of students from the two high schools who completed internships in 2010 divided by the total number of students from the two schools who completed internships that year. Choice C is incorrect. This is the fraction of students from Foothill High School who completed internships out of all the students who completed internships in 2010. Choice D is incorrect. This is the number of students from Valley High School who completed internships in 2010 divided by the number of students from Foothill High School who completed internships in 2010.

Choice D is correct. The table shows that there are a total of 16 kittens that have a chocolate-colored coat. Of the 16 with a chocolate-colored coat, 12 have deep blue eyes. Therefore, the fraction of chocolate-colored kittens with deep blue eyes is simply the ratio of those two numbers, or .Choice A is incorrect; this is the fraction of all chocolate-colored kittens. Choice B is incorrect; this is the fraction of kittens with deep blue eyes that have a chocolate-colored coat. Choice C is incorrect; this is the fraction of cream-tortoiseshell-colored kittens with deep blue eyes.

Choice D is correct. The total number of gas station customers on Tuesday was 135. The table shows that the number of customers who did not purchase gasoline was 50. Finding the ratio of the number of customers who did not purchase gasoline to the total number of customers gives the probability that a customer selected at random on that day did not purchase gasoline, which is .Choice A is incorrect and may result from finding the probability that a customer did not purchase a beverage, given that the customer did not purchase gasoline. Choice B is incorrect and may result from finding the probability that a customer did not purchase gasoline, given that the customer did not purchase a beverage. Choice C is incorrect and may result from finding the probability that a customer did purchase a beverage, given that the customer did not purchase gasoline.

Choice D is correct. If a marble is chosen at random from the bag, the probability of choosing a marble of a certain color is the number of marbles of that color divided by the total number of marbles in the bag. Since there are 10 blue marbles in the bag, and there are 40 total marbles in the bag, the probability that the marble chosen will be blue is .Choices A, B, and C are incorrect. These represent the probability that the marble chosen won’t be blue (choice A), will be green (choice B), and won’t be green (choice C).

Choice A is correct. It’s given that there are 2 hybrid cars priced at no more than $25,000. It’s also given that there are 14 cars total for sale. Therefore, the probability of selecting a hybrid priced at no more than $25,000 when one car is chosen at random is .Choice B is incorrect. This is the probability of selecting a hybrid car priced greater than $25,000 when choosing one car at random. Choice C is incorrect. This is the probability, when choosing randomly from only the hybrid cars, of selecting one priced at no more than $25,000. Choice D is incorrect. This is the probability of selecting a hybrid car when selecting at random from only the cars priced greater than $25,000.

Choice A is correct. The total number of possible outcomes for rolling a fair \(14\)-sided die is \(14\). The number of possible outcomes for rolling a \(2\) is \(1\). The probability of rolling a \(2\) is the number of possible outcomes for rolling a \(2\) divided by the total number of possible outcomes, or \(1 fourteenth\). Choice B is incorrect. This is the probability of rolling a number no greater than \(2\). Choice C is incorrect. This is the probability of rolling a number greater than \(2\). Choice D is incorrect. This is the probability of rolling a number other than \(2\).

The correct answer is . It is given that no contestant received the same score on two different days, so each of the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once. Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants who received a score of 5 on Day 2 or Day 3 by the total number of contestants who received a score of 5, which is given in the table as 7. So the probability is . Note that 5/7, .7142, .7143, and 0.714 are examples of ways to enter a correct answer.