Question

A box contains 6 red and 5 blue marbles. Another box contains 5 red and 8 blue marbles. One box is selected at random and from that bag, one marble is drawn. What is the probability that the marble drawn is blue?

Answer 1

consider each box one at a time

assuming the two boxes are chosen randomly w/ equal probability, the probability of picking one box is (1/2). for the first box, there are 6 red and 5 blue (for a total of 11) so the probability of getting blue for that box is (5/11). the probability of picking this box *and* getting a blue marble is therefore (1/2)*(5/11).

repeat this logic w/ the other box.

then add the two probabilities.