4MA0 Higher June 2014 Paper 4 Q19
19 Amberish plays two games of tennis.
Each time he plays a game of tennis, the probability that he will win is \(\dfrac{2}{7}\)
(a) Complete the probability tree diagram.
(b) Calculate the probability that Amberish wins at least one of the two games of tennis. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{5}{7}\) for does not win | B1 |
| correct binary structure | B1 |
| all labels and values correct | B1 |
| (3) |
Notes
B1: on lower first branch or
on any branch labelled “does not win”
B1: 4 branches needed on RHS
B1: NB. Allow decimals rounded or truncated to 3 or more sig figs \(\left(\dfrac{2}{7} = 0.285714\ldots;\ \dfrac{5}{7} = 0.714285\right)\)
| Scheme | Marks |
|---|---|
| \(\text{“}\tfrac{2}{7}\text{”} \times \text{“}\tfrac{2}{7}\text{”}\) (=0.0813…) or \(\text{“}\tfrac{2}{7}\text{”} \times \text{“}\tfrac{5}{7}\text{”}\) (=0.204…) or \(\text{“}\tfrac{5}{7}\text{”} \times \text{“}\tfrac{2}{7}\text{”}\) | M1 |
| \(\text{“}\tfrac{2}{7}\text{”} \times \text{“}\tfrac{2}{7}\text{”} + \text{“}\tfrac{2}{7}\text{”} \times \text{“}\tfrac{5}{7}\text{”} + \text{“}\tfrac{5}{7}\text{”} \times \text{“}\tfrac{2}{7}\text{”}\) or \(\text{“}\tfrac{2}{7}\text{”} + \text{“}\tfrac{5}{7}\text{”} \times \text{“}\tfrac{2}{7}\text{”}\) | M1 |
| \(\dfrac{24}{49}\) | A1 |
| (3) | |
| (6 marks) |
Notes
M1: ft for any "correct" product; allow decimals only ft probabilities < 1
M1: ft for full method
A1: ft ; allow for decimal answer, accept 0.4897959… truncated or rounded to 3 or more sig figs; only accept 0.49 if preceded by more accurate answer or M2 awarded
or M2 for \(1 - \left(\text{“}\tfrac{5}{7}\text{”}\right)^2\)