Higher November 2021 Paper 2 Q20
20 In a village,
if it rains on one day, the probability that it will rain on the next day is 0.8
if it does not rain on one day, the probability that it will rain on the next day is 0.6
A weather forecaster says,
“There is a 70% chance that it will rain in the village on Monday.”
Work out an estimate for the probability that it will rain in the village on Wednesday.
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.748 | P1 | for a process to find a correct probability product for 2 consecutive days, eg. \(0.7 \times 0.8\) (rain M + T) or \(0.7 \times 0.2\) (rain M + no rain T) or \(0.3 \times 0.6\) (no rain M + rain on T) or \(0.3 \times 0.4\) (no rain M + T) |
| P1 | for process to find a correct triple probability product for it raining on Wednesday, eg. \(0.7 \times 0.8 \times 0.8\) (rain M + T + W) (= 0.448 or \(\dfrac{56}{125}\) oe) or \(0.7 \times 0.2 \times 0.6\) (rain M + no rain T + rain W) (= 0.084 or \(\dfrac{21}{250}\) oe) or \(0.3 \times 0.6 \times 0.8\) (no rain M + rain T + rain W) (= 0.144 or \(\dfrac{18}{125}\) oe) or \(0.3 \times 0.4 \times 0.6\) (no rain M + no rain T + rain W) (= 0.072 or \(\dfrac{9}{125}\) oe) | |
| P1 | for complete process, eg. \(\text{``}0.448\text{''} + \text{``}0.084\text{''} + \text{``}0.144\text{''} + \text{``}0.072\text{''}\) | |
| A1 | oe eg, \(\dfrac{187}{250}\) |
Additional guidance
Throughout accept probabilities given as fractions or percentages
Could be for Tuesday and Wednesday also
NB: correct answer without supportive working gets 0 marks