A bag contains 9 blue marbles and 3 red marbles. One marble is chosen at random from the bag. If this marble is blue, it is replaced back into the bag. If this marble is red, it is not returned to the bag. A second marble is now chosen at random from the bag.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

1. [B1] (3/12) × (2/11) = 6/132 or 1/22 or 0.04545... to at least three significant figures.
2. [M1] (9/12) × (3/12) = 27/144 or 3/16 or 0.1875 seen as numerator or denominator of a fraction.
3. [M1] Their (9/12) × (3/12) + their (3/12) × (2/11) or their 27/144 + their 1/22 seen as denominator of a fraction. FT from part (a).
4. [A1] 33/41 or oe, 0.804878... rounded to at least three significant figures. If A0, SC B1 for correct final answer www.