9709 P52 - Mar 2024 - Q5 - 8 marks
9799
Anil scores 2 for a win, 1 for a draw and 0 for a loss. The respective probabilities are 0.5, 0.3 and 0.2, independently for each game. \(X\) is his total score in the first three games.
(a) Show that \(P(X=2)=0.114\). [2]
(b) Complete the probability distribution table for X. [3]
| \(x\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| \(P(X=x)\) | 0.114 | 0.207 | 0.285 | 0.125 |
(c) Find \(\operatorname{Var}(X)\). [3]
