In a certain country, the weather each day is classified as fine or rainy. The probability that a fine day is followed by a fine day is 0.75 and the probability that a rainy day is followed by a fine day is 0.4. The probability that it is fine on 1 April is 0.8. The tree diagram below shows the possibilities for the weather on 1 April and 2 April. [Figure X.X]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [B1] All probabilities correct, may be on branch or next to 'Fine/Rainy' Ignore additional branches.
2. [M1] Correct or FT from their diagram unsimplified, all probabilities 0<p<1. Partial evaluation only sufficient when correct. Accept working in 4(b) or by the tree diagram.
3. [A1] From supporting working
4. [M1] a×b×c + a × 1-b × d, 0 < c, d ≤ 1, a, b consistent with their tree diagram or correct, no additional terms
5. [A1] At least one term correct, accept unsimplified
6. [A1] Final answer
7. [B1 FT] their (c) + e × f × g + e × (1-f) × h, 0 < g, h < 1, e, f consistent with their tree diagram, or correct
8. [M1] their 4(c) (or correct)/their previously calculated and identified P(Y) or a denominator involving 3 or 4 3-factor probability terms consistent with their tree diagram & third factor 0 <p<1
9. [A1] (0.7458...)