4MA0 Higher June 2016 Paper 3R Q14
14 Linford and Alan race against each other in a competition.
If one of them wins a race, he wins the competition.
If the race is a draw, they run another race.
They run a maximum of three races.
Each time they race, the probability that Linford wins is 0.35
Each time they race, the probability that there is a draw is 0.05
(a) Complete the probability tree diagram.
(b) Calculate the probability that Linford wins the competition. (3)
| Scheme | Marks |
|---|---|
| Correct probabilities | B1 |
| B1ft | |
| (2) |
Notes
B1: For 0.6 on LHS branch
B1ft: For all other probabilities correct
| Scheme | Marks |
|---|---|
| 0.35 + 0.05 × 0.35 + 0.05 × 0.05 × 0.35 oe (=0.35 + 0.0175 + 0.000875) | M2 |
| 0.368375 | A1 |
| (3) |
Notes
M2: ft from tree diagram
M1 for 0.05 × 0.35 or \(0.05^2 \times 0.35\) oe
A1: oe eg \(\dfrac{2947}{8000}\)
Accept 0.36(8375) rounded or truncated to at least 2 SF