Gio has a pack of 18 cards. Ivy has a pack of x cards. Each card has a picture of a bus or a car or a train. The number of cards with each picture in the two packs is shown in the table. Bus | Car | Train Gio's pack | 6 | 10 | 2 Ivy's pack | x-12 | 9 | 3

Mark scheme

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

1. [B1] Either 6/18 * (x-12)/x Or 10/18 * 9/x seen. OE.
2. [B1] Correct equation formed. Fractions may be simplified.
3. [M1] Rearrange probabilities to form quadratic equation and solve to find a value for x. Condone elimination of x on denominators: 6/18 * x(x-12) = 2 * 10/18 * 9 OE. Must be an equation throughout.
4. [A1] If M1 not awarded, SCB1 for [x =] 42 WWW. Note x = 42 must be selected if x = 0 is present.
5. [M1] Two identified un-simplified outcomes with their x substituted. Correct values linked to identified outcomes acceptable (using x = 42).
6. [M1] Add probabilities, 0 < p < 1, for 3 correct scenarios, no incorrect/repeated scenarios. Identification can be implied by un-simplified expressions.
7. [A1] 0.365079... rounded to at least 3SF. OE. [SCB1] 10/42 + 5/42 + 1/126 = 23/63 OE.