A prisoner is exiled to siberia or urals (a mountainious region in russia). The chance of being sent to siberia is 70%. The prisoner knows that a guard in siberia, given randomly selcted, has a probability of .9 to be carrying a AN-94 machine gun, whereas the probability is .6 that the urals will be armed with one.
a) Upon arrival, the first guard whom the prisoner sees is armed with an AN-94. What is the probability that the prisoner has been sent to siberia?
b) Upon arrival, the first guard whom the prisioner sees is armed with an AN-94. What is the probability that the prisioner has been sent to the urals?