# True and false probability question

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

## 1 Answer

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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