a) Cards numbered 1–10 are dealt out in pairs (without replacement). The sum of one person’s pair is 10. What is the probability that both cards contain odd numbers?

b) A soccer team’s star player plays for the full game in 50% of matches, part of the game in 40% and takes no part in the other 10%. When he plays for the full game the probability of a win for his team is 0.7; when he plays for part of the game it is 0.5; when he doesn’t play it is 0.3.

Draw a tree diagram for this data.

Hence calculate (i) the probability of a win for the team; (ii) the probability that he had played for the full match, given that the team won.