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?

Question

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?