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A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice...

A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.

Math   Statistics-And-Probability   
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Answer #1

A = event that one answers the multiple-choice question with 6 possible answers correctly.
B = event that one answers the multiple-choice question with 5 possible answers correctly.
Now, P(A) = Prob.(one answers the multiple-choice question with 6 possible answers correctly) = 1/6.
P(B) = Prob.(one answers the multiple-choice question with 5 possible answers correctly) = 1/5.

Hence, Prob.(both questions are answered correctly) = P(A B) = P(A).P(B) = (1/6) * (1/5) = 1/30.

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