If we have 8 white balls and 5 black balls and one of them is picked at random, the probability of getting a white ball is 8/13. Suppose now we put 3 white balls and 2 black balls in one closed bag and the remaining balls in another identical bag. And now the experiment is that first a bag is chosen at random and then out of it, a ball is picked. Now what is the probability of getting a white ball?
Working it out one way gives one answer and working it out another way gives another ans. If we go by definition of probability here no. of outcomes in event(white balls) doesn't change (ie 8) as well as no of sample points doesn't change (ie 13).So the probability should not change (ie 8/13). But if the Total Probability Theorem is applied (considering choice of 1st bag and choice of 2nd bag as the mutually exclusive and exhaustive events), the answer is 49/80.
The book says the second one is correct (which is agreeable, though counter-intuitive). But what then is the flaw in the first method?
(if there is any other method to obtain a solution pls share)