In: Statistics and Probability
A true-false question is to be posed to a husband-and-wife team on a quiz show. Both the husband and the wife will independently give the correct answer with probability 0.6. the couple uses the following strategy: Have them both consider the question, and then either give the common answer if they agree or, if they disagree, flip a fair coin to determine which answer to give.
What is the conditional probability that the couple gives the correct answer given that the husband and wife agree on the answer?