Finding Probability of Event T?

A court is investigating the possible occurrence of an unlikely event T. The reliability of two independent witnesses Alice and Bob is known to the court: Alice and Bob tell the truth with equal probability p, and there is no collusion between the two of them. Let A and B be the events that Alice and Bob assert... show more A court is investigating the possible occurrence of an unlikely event T. The reliability
of two independent witnesses Alice and Bob is known to the court: Alice and Bob tell the truth with equal probability p, and there is no collusion between the two of them.
Let A and B be the events that Alice and Bob assert (respectively) that T occurred, and let a be the probability that T occurred.

(a) What is the probability that T occurred given that both Alice and Bob declare that T occurred?

(b) Evaluate the probability that T occurred given that both Alice and Bob declare that
T occurred when p = 0.9 and a = 0.001.
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