A plane is missing, and it is presumed that it was equally likely to have gone down in any of 3 possible regions. If the plane is in a given region, the conditional probability that the plane will be found upon a search is 0.6 for region 1, 0.7 for region 2 and 0.8 for region 3. Given that a search in region 1 is unsuccessful, what is the conditional probability (up to 2 decimals) that the plane is in region 1?
I think that I should use the Bayer's Law, the result should be 0.17. Can someone explain to me how can I compute the two probabilities that I need, if my method is correct? Thanks in advance!
P($F_1^c$|1) = P($F^c$|1)
I don't know how to compute $P(F_1^c∣2)$ and $P(F_1^c∣3)$