Sharma knows that she has 3 tins of carrots, 2 tins of peas and 2 tins of sweetcorn in her cupboard. All the tins are the same shape and size, but the labels have all been removed, so Sharma does not know what each tin contains. Sharma wants carrots for her meal, and she starts opening the tins one at a time, chosen randomly, until she opens a tin of carrots. The random variable X is the number of tins that she needs to open.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [M1] m/n × p/q × r/s used throughout. condone use of 1/2
2. [A1] AG. The fractions must be identified, e.g. P(NC, NC, C), may be seen in a tree diagram.
3. [B1] Table with x values and at least one probability Condone any additional x values if probability stated as 0.
4. [B1] One correct probability other than X = 3 linked to the correct outcome
5. [B1] Two further correct probabilities other than X = 3 seen linked to the correct outcome
6. [B1FT] All probabilities correct, or at least 4 probabilities summing to 1
7. [M1] At least 4 correct terms FT their values in (a) with probabilities summing to 1 May be implied by use in Variance, accept unsimplified expression.
8. [M1] Appropriate variance formula using their (E(X))². FT their table accept probabilities not summing to 1.
9. [A1] N.B. If method FT for M marks from their incorrect (b), expressions for E(X) and Var(X) must be seen unsimplified with all probabilities <1