Question

One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow? 

Answer 1

$P=\frac{1}{3}*\frac{3}{11}+\frac{1}{3}*\frac{5}{11}+\frac{1}{3}*\frac{1}{11}=\frac{9}{33}=\frac{3}{11}.$