9709 P61 - Nov 2013 - Q7
2936
James has a fair coin and a fair tetrahedral die with four faces numbered 1, 2, 3, 4. He tosses the coin once and the die twice. The random variable X is defined as follows.
- If the coin shows a head then X is the sum of the scores on the two throws of the die.
- If the coin shows a tail then X is the score on the first throw of the die only.
(i) Explain why X = 1 can only be obtained by throwing a tail, and show that P(X = 1) = \(\frac{1}{8}\).
(ii) Show that P(X = 3) = \(\frac{3}{16}\).
(iii) Copy and complete the probability distribution table for X.
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| P(X = x) | \(\frac{1}{8}\) | \(\frac{3}{16}\) | \(\frac{1}{8}\) |
Event Q is ‘James throws a tail’. Event R is ‘the value of X is 7’.
(iv) Determine whether events Q and R are exclusive. Justify your answer.
