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Jane and Bob are on the same game show. They answer one question, either True or False. The probability that Bob is correct is 70%. The probability that Jane is correct is also 70%. Moreover, the probability that Bob is correct given Jane is either correct or incorrect is still 60%. What is the probability that Bob and Jane are correct given they both give the same answer?

This is how I've done it P(B)=0.70, P(J)=0.70. Then from the third piece of info I have P(B given (J U J')) but that doesn't seem to make sense to me because Bob being correct isn't affected by Jane being correct or not? So is the third statement just P(B n J) + P(B n J') = 0.60 but then isn't that just P(B) which is not 0.60 but 0.70?

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