Kayla has a bag containing 3 red marbles, 1 blue marble and 2 green marbles. She selects one marble from the bag at random and does not replace it in the bag. She repeats this process until she obtains a green marble. The random variable X is the number of marbles that she needs to select until she obtains a green marble.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [B1] Table with correct x values and at least 1 correct probability.
2. [B1] A second correct probability correctly linked to the correct x value, need not be in table, accept un-simplified.
3. [B1] Two more correct probabilities correctly linked to the correct x values, need not be in table, accept un-simplified.
4. [B1] 5 correct probabilities linked with correct x values.
5. [SCB1] 5 non-zero probabilities (not all 1/5) summing to 1 placed in a probability distribution table with correct x values if B1B1 max scored.
6. [SCB2] for X: 0,1,2,3,4 P(X=x): 5/15, 4/15, 3/15, 2/15, 1/15 OE.
7. [M1] Accept un-simplified expression. May be calculated in variance. Accept 1/3 + 8/15 + 3/5 + 8/15 + 1/3 OE for the M mark. FT their table with 5 or 6 probabilities summing to 1 (0 < p < 1).
8. [M1] Appropriate variance formula using their (E(X))^2 value. FT their table with 4 or more probabilities (0 < p < 1) which need not sum to 1 or with an expression no more evaluated than shown in bold.
9. [A1] AWRT. WWW but allow from truncation error (e.g. 0.266 rather than 0.267). Note: 14/9 also comes from SCB2 but scores M1M1A0 max.