Brain Ticklers

There is a 0.25 probability that your friend (call him Bob) took a blue marble. There are two possibilities: Bob took red and you took blue, or Bob and you both took blue. Initially, the bag has 3R and 2B, so there is a 0.6 probability that Bob chose red and a 0.4 probability that he chose blue. You might assume, therefore, that bob's probability of getting a B is 0.4 and that is the answer, but the fact that you drew a B decreases the probability that Bob got a B. If he chose red, that would leave 2R and 2B, and you would have a probability of 0.5 of picking B. Thus, the probability of Bob R, you B is 0.5(0.6) = 0.3. If Bob picked B, then 3R and 1B would be left, and your probability of drawing B would be only 0.25, so the probability of Bob B, you B is 0.25(0.4) = 0.1, and the relative probability is 0.1/(0.1+0.3) =0.25.

~(Honor Society)