Consider 4 indpendent events with the following probabilty of each event occurring: P(A) = 0,4 P(B) = 0,8 P(C) = 0,7 P(D) = 0,2
What is the conditional probabilty of event A and B occurring given that exactly three of the events occur?
OK, so I guess I'm supposed to use Bayes' theorem or something like that, right? I know that in the denomenator the number will be (0,4*0,8*0,7*0,8) + (0,4*0,8*0,3*0,2) + (0,4*0,2*0,7*0,2) + (0,6*0,8*0,7*0,2) since these are the probabilities of all possible "three events occur" situations. However, I am undcertain as to what I should put in the numerator. I guess it would be something like P(three events l A ∩B)*P(A ∩B)). But I really don't know how to calculate this.
Or am I overcomplicating the whole situation?