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a busy cat

I'm stuck on how to do this problem.

Given $p>0$ when husband and wife independently give correct answers

Let $C$ denote the correct answer and $p > 0$, so let $P(C) = p$ and $P($NOT $\,C) = 1 -p$

The probability to get a correct answer is $1/2$.

The probability of them both having the same answer is $1/4$.

Scenario A:

The probability is $1/2$.

Scenario B:

The probability is $1/4$.

So $A$ is better??

I think there is something wrong here.

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but how is it 1/4 if the husband ignore his wife or vise versa – jyuserersh Mar 13 '13 at 7:03

There's no need to calculate. If their answers agree, both strategies lead to the same result. If their answers don't agree, both strategies lead to the correct result with probability $1/2$. For the first strategy, this is because the probability is $1/2$ that it's the designated answerer who has the right answer; for the second strategy, it's because they explicitly choose the answer with probability $1/2$.

Thus the two strategies have the same probability of success.

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