- [Maximum mark: 7]
A fair game is played where points are scored as follows:
• A win scores w points.
• A draw scores 0 points.
• A loss scores –5 points.
Let X be the number of points scored during a game. The probability distribution is shown.
| x | w | 0 | –5 |
|---|---|---|---|
| P(X = x) | 0.25 | 0.4 | p |
(a) Find the value of p. [2]
The game is played 60 times.
(b) Find the expected number of losses. [2]
(c) Calculate the value of w, given that the game is fair. [3]