2016 DHS P2 Q6

John plays for his school’s soccer team. There is a probability of \(0.15\) that he scores in a game and a probability of \(0.3\) that his parents are present at a game. When he scores in a game, there is a probability of \(0.2\) that his parents are present.

1. Show that the probability that he scores in a game when his parents are present is \(0.1\).[2]
2. State, with justification, whether his parents’ presence at a game will affect his chances of scoring in the game.[1]

Games are equally likely to be home or away games. In a home game, there is a probability of \(0.24\) that John does not score and his parents are present.

3. Find the least and greatest values of the probability that a game is a home game and his parents are not present at the game.[3]