Three coins A, B and C are each thrown once. • Coins A and B are each biased so that the probability of obtaining a head is 2/3. • Coin C is biased so that the probability of obtaining a head is 2/5. The random variable X is the number of heads obtained when the three coins are thrown.

Mark scheme

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

1. [M1] One 3 factor probability with 3, 3, 5 as denominators
2. [M1] 3 factor probabilities for 2 or 3 correct scenarios added, no incorrect scenarios
3. [A1] AG, Total of 3 products with clear context
4. [B1] Probability distribution table with correct outcomes with at least one probability, allow extra outcome values if probability of zero stated'
5. [B1] 2 of P(0), P(1) and P(3) correct
6. [B1 FT] 3 or 4 probabilities sum to 1 with P(2) correct
7. [M1] Substitute their attempts at scores in correct variance formula, must have '- mean²' (FT if calculated) (condone probs not summing to 1); must be at least 2 non-zero values
8. [A1] Accept 26 or 27