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Chapter 5: Problem 101

In order to practice law, lawyers must pass the bar exam. In California, the passing rate for first-time bar exam test takers who attended an accredited California law school was \(70 \%\). Suppose two test-takers from this group are selected at random. a. What is the probability that they both pass the bar exam? b. What is the probability that only one passes the bar exam? c. What is the probability that neither passes the bar exam?

Short Answer

Expert verified
The probability that both pass is 0.49, the probability that only one passes is 0.42, and the probability that neither pass is 0.09.

Step by step solution

01

Both Pass

We begin with calculating the probability of both passing. The pass rate is given as 70%, so \(P(\text{pass}) = 0.7\). To find the probability of both passing, we multiply the individual probabilities, since these are independent events. Therefore, \(P(\text{both pass}) = P(\text{first pass}) * P(\text{second pass}) = 0.7 * 0.7 = 0.49\).
02

Only one Passes

Next, we find the probability of only one of them passing. This can happen in two ways: the first person passes and the second fails, or the first person fails and the second passes. The probability of passing is 70% (0.7). The probability of failing is therefore 30% (0.3). Therefore, \(P(\text{only one pass}) = P(\text{first pass and second fail}) + P(\text{first fail and second pass}) = 2* (0.7 * 0.3) = 0.42\).
03

Neither Passes

Finally, we find the probability of neither of them passing. This is similar to both passing. The probability of failing is 30%, hence \(P(\text{neither passes}) = P(\text{first fails}) * P(\text{second fails}) = 0.3 * 0.3 = 0.09\).

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