Probability question

2011-03-17 1:06 am

Please explain:
40 students take the test and 10 do not prepare.
Assume the students who have prepared for the test can pass the test.
Probability of any student who do not prepare but pass the test = 0.0376
(a) If 2 students are selected from the class at random, find the probability that both of them pass the test. (Ans=0.572)
(b) If 2 students are selected from the class at random, find the probability that at least one of them does not prepare for the test given that both of them pass the test. (Ans=0.0254)

回答 (1)

myisland8132

2011-03-17 1:20 am

✔ 最佳答案

(a) P(both of them pass the test)

= [(10C2)(0.0376)^2 + (10C1)(30C1)(0.0376) + (30C2)]/(40C2)

= 0.572

(b) P(At least one of them does not prepare for the test | both of them pass the test)

= {[(10C2)(0.0376)^2 + (10C1)(30C1)(0.0376)]/(40C2)}/0.572= 0.0254

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