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a busy cat Im stuck on how to do this problem

Given P>0 when husband and wife independently give correct answers

C = correct answer

and p > 0

so Lets 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 1

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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