A box contains 6 identical-sized discs, of which 4 are blue and 2 are red. Discs are taken at random from the box in turn and not replaced. Let X be the number of discs taken, up to and including the first blue one.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. EITHER: (M1 probabilities in order 2/6 x 1/5 x 4/4, p, q, r ≤ 6 and p≥ q ≥ r, r ≥4, accept × 1 as 4/r
2. A1) Needs either P(RRB) OE stated or identified on tree diagram.
3. OR1: (M1 probabilities stated clearly, 2C2/6C2 x 4C1/4C1 or x 1 or x 4/4 included
4. A1) Needs either P(RRB) OE stated or identified on tree diagram.
5. OR2: (M1 probabilities in order 2C1/6C1 x 1C1/5C1 x 4C1/4C1, p. q. r ≤6 and p≥q≥r, r≥4 (x 4C1/4C1 or x 1 or x 4/4 acceptable)
6. A1) Needs either P(RRB) OE stated or identified on tree diagram.
7. B1 Probability distribution table drawn with at least 2 correct x values and at least 1 probability. All probabilities 0 <p<1.
8. B1 P(1) or P(2) correct unsimplified, or better, and identified.
9. B1 All probabilities in table, evaluated correctly OE. Additional x values must have a stated probability of 0