A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random variable X denotes the number of blue marbles selected.

Mark scheme

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

1. [M1] AG. Method 1: (6/10) x (5/9) x (4/8) x (3/7) x 4!/(2!2!) or (6/10) x (5/9) x (4/8) x (3/7) x k for k an integer, k > 1. Method 2: ⁶C2 x ⁴C2 seen as the numerator of a fraction. Condone use of permutations if used consistently.
2. [A1] AG. ⁴C2 may be seen for 4!/(2!2!).
3. [B1] Table with correct values of x and at least one further non-zero probability correct. Condone extra x values if probability stated as 0.
4. [B1] Third probability correct. Accept probabilities not in table if clearly identified.
5. [B1] Fourth probability correct. Accept probabilities not in table if clearly identified.
6. [B1] Fifth probability correct. Accept probabilities not in table if clearly identified. SCB1 for 4 further non-zero probabilities adding to 4/7, 0.5712 if B2 max scored.
7. [M1] 3/7 + 8/21 + their 8/21 seen as the numerator of a fraction.
8. [B1 FT] (4/35 + 3/7 + 8/21 + their 8/21) seen as the denominator of a fraction.
9. [A1] Accept 0.87628... to at least 3SF.