Understanding Conditional Probability: SAT Math Practice Guide
School
Valley High School**We aren't endorsed by this school
Course
ENGLISH 102
Subject
Statistics
Date
Dec 10, 2024
Pages
20
Uploaded by AdmiralTitanium8881
7/9/24, 2:58 AMPage 1 of 20about:srcdoc
7/9/24, 2:58 AMPage 2 of 20about:srcdocQuestion ID e29586d5ID: e29586d5Number of Contestants by Score and Day5 outof 54 outof 53 outof 52 outof 51 outof 50 outof 5TotalDay123462320Day223554120Day333453220Total7913169660The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1point for each correct answer. The number of contestants receiving a given score on each day is shown in the tableabove.No contestant received the same score on two different days. If a contestant isselected at random, what is the probability that the selected contestantreceived a score of 5 on Day 2 or Day 3, given that the contestant received ascore of 5 on one of the three days?ID: e29586d5 AnswerRationaleThe correct answer is . It is given that no contestant received the same score on two different days, so each of thecontestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once. Therefore, theprobability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the contestant received ascore of 5 on one of the three days, is found by dividing the total number of contestants who received a score of 5 onDay 2 or Day 3 by the total number of contestants who received a score of 5, which is given in the table as7. So the probability is . Note that 5/7, .7142, .7143, and 0.714 are examples of ways to enter a correct answer.AssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 3 of 20about:srcdocQuestion Difficulty:Hard
7/9/24, 2:58 AMPage 4 of 20about:srcdocQuestion ID b1b5300bID: b1b5300bPrices of 14 Different CarsType of carPriced at no morethan $25,000Priced greaterthan $25,000TotalNonhybrid538Hybrid246Total7714The table above shows information about 14 cars listed for sale on an auto dealership’s website. If oneof the cars listed for sale is selected at random, what is the probability that the car selected will be ahybrid car priced at no more than $25,000 ?A. B. C. D. ID: b1b5300b AnswerCorrect Answer:ARationaleAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 5 of 20about:srcdocChoice 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 are14 cars total for sale. Therefore, the probability of selecting a hybrid priced at no more than $25,000 when one car ischosen at random is .Choice B is incorrect. This is the probability of selecting a hybrid car priced greater than $25,000 when choosing onecar at random. Choice C is incorrect. This is the probability, when choosing randomly from only the hybrid cars, ofselecting one priced at no more than $25,000. Choice D is incorrect. This is the probability of selecting a hybrid carwhen selecting at random from only the cars priced greater than $25,000.Question Difficulty:Medium
7/9/24, 2:58 AMPage 6 of 20about:srcdocQuestion ID e1ad3d41ID: e1ad3d41Coat colorEye colorDeep blueLight brownTotalCream-tortoiseshell161632Chocolate12416Total282048The data on the coat color and eye color for 48 Himalayan kittens available foradoption were collected and summarized in the table above. What fraction ofthe chocolate-colored kittens has deep blue eyes?A. B. C. D. ID: e1ad3d41 AnswerCorrect Answer:DRationaleChoice D is correct. The table shows that there are a total of 16 kittens that have a chocolate-colored coat. Of the 16AssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 7 of 20about:srcdocwith a chocolate-colored coat, 12 have deep blue eyes. Therefore, the fraction of chocolate-colored kittens with deepblue 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 ofkittens 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.Question Difficulty:Medium
7/9/24, 2:58 AMPage 8 of 20about:srcdocQuestion ID d4413871ID: d4413871Blood type Rhesus factorABABO339337721xHuman blood can be classified into four common blood types—A, B, AB, and O.It is also characterized by the presence or absence of the rhesusfactor. The table above shows the distribution of blood type and rhesus factorfor a group of people. If one of these people who is rhesus negative ischosen at random, the probability that the person has blood type B is . Whatis the value of x?ID: d4413871 AnswerRationaleThe correct answer is 8. In this group, of the people who are rhesus negative have blood type B. The total number ofpeople who are rhesus negative in the group is , and there are 2 people who are rhesus negative withblood 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 thisequation by yields . Subtracting 10 from both sides of this equation yields .Question Difficulty:HardAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 9 of 20about:srcdocQuestion ID 0301c5dcID: 0301c5dcThe table below shows the number of state parks in a certain state that contain camping facilities and bicyclepaths.Has bicycle pathsDoes not have bicycle pathsHas camping facilities205Does not have camping facilities84If one of these state parks is selected at random, what is the probability that ithas camping facilities but does not have bicycle paths?A. B. C. D. ID: 0301c5dc AnswerCorrect Answer:ARationaleAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 10 of 20about:srcdocChoice A is correct. The total number of state parks in the state is . According to the table, 5 ofthese have camping facilities but not bicycle paths. Therefore, if a state park is selected at random, the probability thatit has camping 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 campingfacilities does not have bicycle paths. Choice C is incorrect. This is the probability that a state park selected at randomfrom the state parks with bicycle paths does not have camping facilities. Choice D is incorrect. This is the probabilitythat a state park selected at random from the state parks without bicycle paths does have camping facilities.Question Difficulty:Medium
7/9/24, 2:58 AMPage 11 of 20about:srcdocQuestion ID 2df8f293ID: 2df8f293Each vertex of a -sided polygon is labeled with one of the letters through , with a different letter at eachvertex. If one vertex is selected at random, what is the probability that the letter will be at the selected vertex?(Express your answer as a decimal or fraction, not as a percent.)ID: 2df8f293 AnswerCorrect Answer:.0714, 1/14RationaleThe correct answer is 114. If one vertex of the polygon is selected at random, the probability that the letter will be atthe selected vertex is equal to the number of vertices labeled with the letter divided by the total number of vertices.It's given that each vertex is labeled with one of the 14letters through , with a different letter at each vertex. Itfollows that there is 1vertex labeled with the letter . It's also given that the polygon is 14-sided. It follows that thereare a total of 14vertices. Thus, the probability that the letter will be at the selected vertex is 114. Note that 1/14, .0714,and 0.071 are examples of ways to enter a correct answer.Question Difficulty:MediumAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 12 of 20about:srcdocQuestion ID 6626cac3ID: 6626cac3Phone EmailDinnerdance55%80%Footballgame20%10%Picnic20%5%Poolparty5%5%Total100%100%An alumni association survey asked each high school graduate to select the one activity he or shepreferred for the association’s next event. Some of the people responded by phone, and the othersresponded by email. The table above shows the distribution of preferred activity, in percent, for eachresponse type used. For the survey, the number of email responses was twice the number of phoneresponses. If a person who preferred a picnic is selected at random, what is the probability that theperson responded by email?ID: 6626cac3 AnswerRationaleAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 13 of 20about:srcdocThe 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 a picnic. It follows that the expression represents the number ofthese people. The table also shows that 5% of the people who responded by email preferred a picnic. The expression , or , represents the number of these people. Therefore, a total of , or peoplepreferred a picnic. Thus, the probability of selecting at random a person who responded by email from the people whopreferred a picnic is , or . Note that 1/3, .3333, and 0.333 are examples of ways to enter a correct answer.Question Difficulty:Hard
7/9/24, 2:58 AMPage 14 of 20about:srcdocQuestion ID 585de39aID: 585de39aOn May 10, 2015, there were 83 million Internet subscribers in Nigeria. Themajor Internet providers were MTN, Globacom, Airtel, Etisalat, and Visafone. BySeptember 30, 2015, the number of Internet subscribers in Nigeria hadincreased to 97 million. If an Internet subscriber in Nigeria on September 30,2015, is selected at random, the probability that the person selected was anMTN subscriber is 0.43. There were pmillion MTN subscribers in Nigeria onSeptember 30, 2015. To the nearest integer, what is the value of p ?ID: 585de39a AnswerRationaleThe correct answer is 42. It’s given that in Nigeria on September 30, 2015, the probability of selecting an MTNsubscriber from all Internet subscribers is 0.43, that there were p million, or , MTN subscribers, and thatthere were 97 million, or 97,000,000, Internet subscribers. The probability of selecting an MTN subscriber from allInternet subscribers can be found by dividing the number of MTN subscribers by the total number of Internetsubscribers. Therefore, the equation can be used to solve for p. Dividing 1,000,000 from thenumerator and denominator of the expression on the left-hand side yields . Multiplying both sides of thisequation by 97 yields , which, to the nearest integer, is 42.Question Difficulty:HardAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 15 of 20about:srcdocQuestion ID 912cd125ID: 912cd125For a science project, Anka recorded whether it rained each weekday and weekend day for 12 weeks. Her results aresummarized in the table below.Weekday and Weekend Day Rain for 12 WeeksRainNo rainTotalNumber of weekdays124860Number of weekend days81624Total206484If one of the days on which there was no rain is selected at random, what is theprobability the day was a weekend day?A. B. C. D. ID: 912cd125 AnswerCorrect Answer:BRationaleAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 16 of 20about:srcdocChoice 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 ofthe days with no rain were weekend days. Because the day is selected at random, each day has an equal chance ofbeing 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 isa weekend day with no rain. Choice C is incorrect. It is the probability that a day selected at random from the weekenddays has no rain. Choice D is incorrect. It is the probability that a day selected at random from the days with no rain is aweekday.Question Difficulty:Medium
7/9/24, 2:58 AMPage 17 of 20about:srcdocQuestion ID 6a715bedID: 6a715bedThe table summarizes the distribution of age and assigned group for participants in a study.–years–yearsyearsTotalGroup AGroup BGroup CTotalOne of these participants will be selected at random. What is the probability of selecting a participant from group A,given that the participant is at least years of age? (Express your answer as a decimal or fraction, not as a percent.)ID: 6a715bed AnswerCorrect Answer:.3833, 23/60RationaleThe correct answer is 2360. It's given that one of the participants will be selected at random. The probability of selecting aparticipant from group A given that the participant is at least 10years of age is the number of participants in group Awho are at least 10years of age divided by the total number of participants who are at least 10years of age. The tableshows that in group A, there are 14participants who are 10–19years of age and 9participants who are 20 +years ofage. Therefore, there are14 + 9, or 23, participants in group A who are at least 10years of age. The table also showsthat there are a total of 30participants who are 10–19years of age and 30participants who are 20 +years of age.Therefore, there are a total of 30 + 30, or 60, participants who are at least 10years of age. It follows that the probabilityof selecting a participant from group A given that the participant is at least 10years of age is 2360. Note that 23/60,.3833, and 0.383 are examples of ways to enter a correct answer.Question Difficulty:HardAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 18 of 20about:srcdocQuestion ID 30db8f77ID: 30db8f77At a conference, there are a total of attendees. Each attendee is assigned to either group A, group B, or group C. Ifone of these attendees is selected at random, the probability of selecting an attendee who is assigned to group A is and the probability of selecting an attendee who is assigned to group B is . How many attendees areassigned to group C?ID: 30db8f77 AnswerCorrect Answer:88RationaleThe correct answer is 88. It's given that there are a total of 275attendees and each attendee is assigned to either groupA, group B, or group C. It's also given that if one of these attendees is selected at random, the probability of selecting anattendee who is assigned to group A is 0.44and 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, attendeeswho are assigned to group B. The number of attendees who are assigned to group C is the number of attendees whoare not assigned to group A or group B. In other words, the number of attendees who are assigned to group C is thetotal number of attendees minus the number of attendees who are assigned to group A and group B. Therefore, thenumber of attendees who are assigned to group C is 27512166, or 88.Question Difficulty:MediumAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 19 of 20about:srcdocQuestion ID 38a9ac45ID: 38a9ac45If 1,200 customers register for new accounts at a social media website everyday, what fraction of the first 60,000 new accounts are registered in the first 5days?A. B. C. D. ID: 38a9ac45 AnswerCorrect Answer:BRationaleChoice B is correct. If 1,200 customers register for new accounts every day, then (1,200)(5) = 6,000 customersregistered 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 fractionrepresents the fraction of accounts registered in 1 of the first 5 days. Choice C isincorrect and may result from conceptual or computation errors. Choice D is incorrect. The fractionrepresents thefraction of the first 60,000 accounts that were registered in 1 day.Question Difficulty:MediumAssessmentSATTestMathDomainProblem-Solvingand Data AnalysisSkillProbability andconditionalprobabilityDifficulty
7/9/24, 2:58 AMPage 20 of 20about:srcdoc