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380 CHAPTER 5 PROBABILITY (a) Find the probability that all 4 calls are four medical help. (2) Suppose we randomly select one of the subjects from the experiment. Show that the events "Diet B" and (b) What's the probability that at least I of the calls is not "Lost weight" are independent. for medical help? ( b ) Copy and complete the table so that there is no amo. (e) Explain why the calculation in part (a) may not be ciation between type of diet and whether a subject boy valid if we choose 4 consecutive calls to the station. weight. 96. Broken links Internet sites often vanish or move so (e ) Copy and complete the table so that there is an asso. that references to them can't be followed. In fact, 87% ciation between type of diet and whether a subject lost of Internet sites referred to in major scientific journals weight. still work within two years of publication. Suppose we 99. Checking independence Suppose A and B are randomly select 7 Internet references from scientific two events such that P(A) = 0.3, P(B) = 0.4, and journals. P(AnB) = 0.12. Are events A and B independent? (a) Find the probability that all 7 references still work two Justify your answer. years later. 100. Checking independence Suppose C and D are (b) What's the probability that at least 1 of them doesn't two events such that P(C) = 0.6, P(D) = 0.45, and work two years later? P(CnD) = 0.3. Are events C and D independent? Justify your answer. (c) Explain why the calculation in part (a) may not be valid if we choose 7 Internet references from one issue 101. The geometric distributions You are tossing a pair of of the same journal. fair, six-sided dice in a board game. Tosses are inde- 97. Mutually exclusive versus independent The two-way pendent. You land in a danger zone that requires you table summarizes data on the gender and eye color of to roll doubles (both faces showing the same number students in a college statistics class. Imagine choosing of spots) before you are allowed to play again. a student from the class at random. Define event A: (a) What is the probability of rolling doubles on a single student is male, and event B: student has blue eyes. 27 toss of the dice? Gender ( b) What is the probability that you do not roll doubles on Male Female Total the first toss, but you do on the second toss? Blue What is the probability that the first two tosses are Eye color 10 (c) Brown 40 not doubles and the third toss is doubles? This is the Total 20 30 50 probability that the first doubles occurs on the third toss. (d) Do you see the pattern? What is the probability that (a) Copy and complete the two-way table so that events A and B are mutually exclusive. the first doubles occurs on the kth toss? 102. Matching suits A standard deck of playing cards (b) Copy and complete the two-way table so that events A consists of 52 cards with 13 cards in each of four suits. and B are independent. spades, diamonds, clubs, and hearts. Suppose you (c) Copy and complete the two-way table so that shuffle the deck thoroughly and deal 5 cards face-up events A and B are not mutually exclusive and not onto a table. independent. (a) What is the probability of dealing five spades in a row? 98. Independence and association The two-way table sum- (b ) marizes data from an experiment comparing the effect Find the probability that all 5 cards on the table have the same suit. tiveness of three different diets (A, B, and C) on weight loss. Researchers randomly assigned 300 volunteer subjects to the three diets. The response variable was Multiple Choice: Select the best answer for Exercises 103-106. whether each subject lost weight over a 1-year period 103. An athlete suspected of using steroids is given two test Diet that operate independently of each other. Test A has B probability 0.9 of being positive if steroids have been C Total used. Test B has probability 0.8 of being positive if Lost weight? Yes 60 80 steroids have been used. What is the probability that No 40 120 neither test is positive if the athlete has used steroids? Total 90 100 110 300 (a) 0.08 (b) 0.28 (c) 0.02 (d) 0.38 (e) 0.72