A sports event is taking place for 4 days, beginning on Sunday. The probability that it will rain on Sunday is 0.4. On any subsequent day, the probability that it will rain is 0.7 if it rained on the previous day and 0.2 if it did not rain on the previous day.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] [P(no rain) = 0.6×(0.8)³ =] 0.3072, 192/625. Exact value required.
2. [M1] 0.6×0.8×0.2. a × b × c where a, b = 0.6, 0.8, c = 0.2, 0.4, 0.7. Condone including Wednesday with both 0.3 and 0.7 used.
3. [A1] = 0.096[0], 12/125.
4. [B1] Correct probability for one clearly identified outcome evaluated accept unsimplified. A correct unsimplified expression is not sufficient.
5. [M1] Add 4 probability values, 0 < p < 1, for appropriate identified scenarios. Accept unsimplified. Ways of identifying scenarios for this mark: Stating the days. All the unsimplified probability calculations exactly as stated in the mark scheme. Identifying the correct branches on a tree diagram and linking with the values. No repeated scenarios. No incorrect scenarios.
6. [A1] 0.2112, 132/625. Accept 0.211. If 0/3 scored SC B1 for 0.2112, 132/625.