Suppose that the continued survival of GM depends on the state of the

economy next year. Assume that the probability of a recovery next year is

0.2, the probability of slow growth is 0.4 and the probability of remaining in

recession is 0.4. If the economy is in recovery, the probability that GM

declares bankruptcy is 0.1; if the economy is experiencing slow growth, the

probability that GM declares bankruptcy is 0.3, and if the economy is in

recession, the probability that GM declares bankruptcy is 0.8. If GM

declares bankruptcy, what is the probability that the economy is in

recession?