A game consists of randomly choosing a bag (labelled 1, 2 or 3) out of a choice of 100, and then again randomly, picking a ball (red or black) from it. Each bag has the same total number of balls (10)

a) complete the tree diagram

b) Work out the probability that a player will select a red ball

c) the same player is going to play the game 200 times consecutively. How many black balls should he expect to pick?