A journalist has received a message from a source stating an astonishing claim about the mayor.

Currently, the journalist believes that the claim is true with a probability of 5/7. The problem is that the sources integrity and motives are questionable, and so before publishing story, the journalist will consult with a second source [referred to as the mouth] who will give an opinion (either belief or disbelief in the claim). The journalist believes that the mouth will believe the claim with a probability of 0.7.

In past situations where the mouth reviewed questionable stories which ultimately turned out to be true, he believed them with a probability of 0.9, while in past situations where questionable stories turned out to be false, the mouth did not believe them with a probability of 0.8.

A. Let T be the event that the claim is true and B be the event that the mouth expresses belief in the claim. Use Bayes theorem to find the probabilities: p(T|B), p(T|B`), p(T`|B), and p(T`|B`).

Please show all work.