A chess player who plays with white pieces will win any particular game with

probability 0.4, draw with probability 0.4, and lose with probability 0.2. The

corresponding probabilities when she plays with black pieces are 0.2, 0.5 and

0.3, respectively. Before each game a fair coin is tossed to decide whether she

will play with the black pieces or the white pieces. Hence the probability she

plays with the white pieces is 0.5. Assume that the results of different games

are independent.

i. Given that she won her last game, what is the probability she was playing

with the white pieces?

(2 marks)

ii. Given that she did not lose either of her last two games, what is the

probability she was playing with the same colour of pieces in both games?

(3 marks)

iii. Considering the next 10 games, what could you say about the distribution

of the number of these games that she wins? Your answer should include

a sketch plot of the probability distribution.