A radar unit picks up a mixture of a legitimate signal and noise with probability p, and noise alone ...

A radar unit picks up a mixture of a legitimate signal and noise with probability p, and noise alone with probability 1 - p. If a legitimate signal arrives with noise, then the unit registers the presence of a signal with probability p1. If the noise alone arrives, then the unit registers the presence of a signal with probability p2. The unit is known to have registered the presence of a signal. Find the probability that there was a legitimate signal.