Andrei Markov, a Russian spy, has three Americans – Joe, John, and Jim – under surveillance. Each man owns one and only one car. Markov knows that the three cars are painted blue, black, and brown respectively, but does not know which man owns which car. After considerable snooping, he estimates the probabilities of each man owning each of the cars as follows:
Car Blue Black Brown Joe .5 0 .5 John .25 .25 .5 Jim .25 .75 0
After Markov has determined three probabilities, Kolmogorov a trusted informer, tells him that Joe owns the brown car. With this information, what is the probability that Jim owns that black car?
이게 각각의 사건이 독립이 아니라서 도대체 어떻게 해야 할지 난감하네요, 부탁드려요!!! ㅠ