Higher November 2024 Paper 1 Q19
19 In the semi-finals of a chess tournament,
player A will play player B
and player C will play player D.
The two winners will then play each other in the final.
The probability that player A will win against player B is 0.6
The probability that player A will win against player C is 0.5
The probability that player A will win against player D is 0.3
The probability that player C will win against player D is 0.2
Work out the probability that player A will win the chess tournament. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.204 | P1 | for a process to find a correct product, eg P(A plays C in the final) \(= 0.6 \times 0.2\ (= 0.12)\) or P(A plays D in the final) \(= 0.6 \times 0.8\ (= 0.48)\) or P(A wins against B and C) \(= 0.6 \times 0.5\ (= 0.3)\) or P(A wins against B and D) \(= 0.6 \times 0.3\ (= 0.18)\) |
| P1 | for a process to find the probability of A winning against C or winning against D in the final, eg P(A wins against C in the final) \(= \text{``}0.12\text{''} \times 0.5\ (= 0.06)\) or P(A wins against D in the final) \(= \text{``}0.48\text{''} \times 0.3\ (= 0.144)\) or P(A wins against C in the final) \(= \text{``}0.3\text{''} \times 0.2\ (= 0.06)\) or P(A wins against D in the final) \(= \text{``}0.18\text{''} \times 0.8\ (= 0.144)\) | |
| P1 | for a complete process, eg P(A wins the tournament) \(= \text{``}0.06\text{''} + \text{``}0.144\text{''}\) | |
| A1 | for 0.204 oe |
Additional guidance
Could work with fractions
Could be seen as part of a correct triple product