## Probability Trees Exercise

1. A bag contains 7 blue balls and 3 yellow balls. Two balls are drawn at random.

 (a) Copy and complete the probability tree diagram. (b) What is the probability of two blue balls being selected? (c) What is the probability of balls of different colours being selected? (d) What is the probability of both of the balls not being yellow? 2. The probability that a train is late at a certain station on a Thursday morning is 1/4. If the train is late on Thursday, the probability that it is also late on Friday is 1/12, but if it is on time on Thursday the probability that it is late on Friday is 1/4.

 (a) Copy and complete the probability treebelow to show this information. (b) What is the probability that the trainis late on both days? (c) What is the probability that the train islate on one day and on time on the other day? (d) What is the probability that the trainis on time on both days? 3. David and Hayden play two games of tennis. The probability of David winning the first game is 1/3.
If he wins the first game, the probability of him winning the second game is 2/3, but if he loses the first game the probability of him losing the second game is 1/2.

 (a) Draw a probability tree for these two games. (b) What is the probability of David winning both games? (c) What is the probability of David losing both games? (d) What is the probability of Hayden winning one game and losing one game? 