Extra Review Ch. 6 AP STATS Name________________ Date________Per______ CHAPTER 6 MC 1. The Conditional probability that the event E Occurs given the event F has occurred is P( E F ) P( E ) P( E F ) b. P( E ) P( E F ) c. P( F ) P( E F ) d. P( F ) 2. If P(A) =.5,P(B) =.3 and P( A B) = .15,then a. A and B are disjointed events. b. A and B are independent events. c. A and B are dependent events. d. A and B are mutually exclusive events. 3. Which of the following is not a probability rule? a. P(A) = 1- P( A c ) a. b. P( A B) P( A) P( B A). c. P( A B) P( A) P( B) P( A B). d. P( A B) P( A) P( B). If disjoint. 4. If a fair coin is flipped twice with the outcome of each flip independent of each other, then the probability that at least one of the two flips results in a head is a. ¼ c. ¾ b. ½ d. 1 5. Only twenty percent of the applicants for new positions at a large software company are female. Assuming that two positions will be filled independently of each other, what is the probability that both positions are filled by females? a. .36 c. .96 b. .64 d. .04 6. Two events A and B are said to be independent when a. P( A) 1 P( B) c. P( A B) P( A) b. P( A B) P( B) d. P( A B) P( A) P( B) 7. A family is going shopping for a new van. The probability that the family will purchase a Ford van is .33, a Chevy van .25, a Dodge van .20, and Toyota van .22. The probability that the family purchases a Toyota van or a Ford van or a Chevy van is a. .33 .22 .25 c. 1- .33 .22 .25 b. .33+ .22+ .25 d. 1- (.33+.22+.25) 8. Suppose there are 60 students in a statistics class of which 24 are female. If three students are selected without replacement to work problems at the board, what is the probability that all 3 of the students chosen are female? a. 24/60+23/59+22/58 c. 24/60 23/59 22/58 b. 24/60+23/60+22/60 d. 1-24/60 23/59 22/58 9. The probability that a new tire will have a blowout in the first year is .10. If the four tires on a new car function independently of each other, what is the probability that at least one tire blows out in the first year? a. .10 .10 .10 .10 c. .90 .90 .90 .90 b. 1-(.10 .10 .10 .10) d.1-(.90 .90 .90 .90) 10. For a random sample of size n taken from a population of size N, independence can be assumed for purposes of calculation of probabilities when a. n is no larger than 5% of N c. n is no larger than 50% of N b. n is at least 5% of N d. n is at least 50% of N CHAPTER 6 SHORT ANSWER: 11. Explain what it means for two events to be independent. 12. Under what conditions is the probability that event A or event B occurs equal to the sum of their probabilities? 13. Under what conditions is the probability that both events A and B occur equal to the product of their probabilities? 14. A paranormal researcher is studying ESP and has developed a test consisting of 5 independent items. She has simulated the probabilities of getting 0, 1, 2, 3, 4, or 5 of the test items correct by guessing and has constructed the following distribution. # Correct 0 1 2 3 4 5 Frequency 28 151 308 317 163 33 a. Estimate the probabilities of getting 0, 1, 2, 3, 4, or 5 correct when a person taking the test guesses on each item. b. Estimate the probability that a person taking the test by guessing at each item gets at least 3 correct. ______ c. Using the estimated probabilities, do you believe that a person who gets all 5 items correct is guessing? Explain. 15. A large manufacturing company runs day and night work shifts in producing their product. The day shift produces 60% of the product and the night shift 40% of the product. Furthermore, 5% of the product is defective given that it was produced during the day shift and 2% is defective given that it was produced during the night shift. Tree Diagram: a. Determine the probability that a defective product is produced by this company. ______ b. Determine the probability that the day shift produced the product given that it is defective. ______ c. Determine the probability that the night shift produced the product given that it is defective. 16. Two different types of Pokemon are used in a battle with 42% of the time a Water type being used and 58% of the time a Fire type is used. Suppose that the probability that you win the battle is .87 given a Water type is used and .55 given a Fire type is used. Tree Diagram: a. Determine the probability that you win the battle. ______ b. Given that you won the battle, what is the probability that a Fire type was used? ______ c. What is the probability that a Water type was used, given that you lost the battle,? ______ 17. Suppose P(A)= .60, P(B) = .80 and P( A B) = .45 Determine a. P( Ac ) =______ c. P( A B) =_______ b. P( A B) =_______ 18. d. whether A and B are independent events.______ Mr. H has developed a new volleyball serve that aces his opponent 77% of the time. If two serves are taken independently of each other, what is the probability that a. both serves are aces? ______ b. at least one serve is an ace? ______ 19. Suppose P(A)=.25, P(B) = .37 and P(C)= .18 Determine a. P( A B C ) when A, B, C are mutually exclusive. b. P( A B C ) when, A, B, C are mutually independent. ______ ______ Answers: Ch. 6: 1) D 2) B 3) B 4) C 5) D 6) C 7) B 8) C 9) D 10) A 11) Two events are independent if the knowledge of event A does not change the outcome of event B 12) When the two events cannot occur simultaneously. 13) When the two events are independent. 14) a. .028, .151, .308, .317, .163, .033 b. .513, c. no, it is unlikely to get all 5 correct by guessing. 15) a. .038 b. .789 c. .211 16) a. .6844 b. .4661 c. .173 17) a. .40 b. .5625 c. .95 d. no .6 .5625 18) a. .5929 b. .9471 19) a. .8 b. .0167