A game is played with 3 coins, A, B and C. Coins A and B are biased so that the probability of obtaining a head is 0.4 for coin A and 0.75 for coin B. Coin C is not biased. The 3 coins are thrown once.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [5] B1 0, 1, 2, 3 seen as top line of a pdf table OR attempting to evaluate P(0), P(1), P(2) and P(3)
2. [5] M1 Multiply 3 probabilities together from 0.4 or 0.6, 0.25 or 0.75, 0.5 with or without a table
3. [5] M1 Summing 3 probabilities for P(1) or P(2) with or without a table
4. [5] B1 One correct probability seen.
5. [5] A1 All correct in a table
6. [3] M1 Correct unsimplified expression for the mean using their table, ∑p = 1; can be implied by correct answer
7. [3] M1 Correct unsimplified expression for the variance using their table and their mean² subtracted, ∑p = 1
8. [3] A1 Correct answer