There are two identical boxes of balls. In the first box 2 blue and 5 orange balls, and the second 3 blue and 6 orange balls. Chosen at random from the box and pull out a 1 ball. What is the probability that the ball taken is orange

Answer 1

2 cases:
box 1, then orange
box 2, then orange

prob = (1/2)(5/7) + (1/2)(6/9)
= 5/14 + 6/18 = 29/42