2 In a game of darts, a player throws three darts. Let \(X\) represent the number of darts which hit the bull's-eye. The probability distribution of \(X\) is shown in the table.
| \(r\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = r )\) | 0.5 | 0.35 | \(p\) | \(q\) |
- (A) Show that \(p + q = 0.15\).
(B) Given that the expectation of \(X\) is 0.67 , show that \(2 p + 3 q = 0.32\).
(C) Find the values of \(p\) and \(q\). - Find the variance of \(X\).