1. If two dice are tossed
a. What is the probability that the sum is 7?
b. What is the probability that the sum is 7, given that the first die is 3?
c. What is the probability that the first die is 3, give that the sum is 7?
d. What is the probability that the first die is 3, give that the sum is 5?
2. In the 2000 Summer Olympics, the head of the Australian drug testing said that the odds of the lab giving a positive result on a negative sample for an athlete was about 1 in 1000, or about .1%. Suppose that the tests are 100% accurate on positive samples (so they will all test positive), and that 5% of the athletes are actually using drugs. What is the conditional probability that an athlete who tested positive for drug use, actually had a positive sample? What would be the conditional probability if 1% of the athletes had positive samples?
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The most straightforward approach is to identify how many cases with sum 7 can occur among the total number of possibilities, which is 6*6=36 (since any number from each of the two dice is equally likely to appear when rolling).
Sum 7 can be obtained in 6 situations, namely: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. Then the probability to obtain 7 is 6/36= 1/6....
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