A bag contains 4 blue marbles and 12 red marbles. One marble is selected at random from the bag. If this marble is blue, it is replaced in the bag, but if it is red, it is not replaced. A second marble is now selected at random from the bag.

Mark scheme

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

1. [M1] OE. (4/16 x 4/16) and either (12/16 x 11/15) or (12/16 x 12/16) seen. Decimals to 4SF but condone (11/15) = 0.733. No additional terms.
2. [A1] ISW. CAO, (0.6125, 49/80 must be seen). If M mark not scored, SCB1 for 49/80 ,0.6125 WWW.
3. [M1] (4/16 x 12/16) seen as a numerator of a single fraction. If 0.1875 or 3/16 is seen as the numerator, the calculation must be seen in the working for the denominator – or in 3(a), including by the tree diagram. The question will need to be linked if the work is in 3(a).
4. [M1] {their (4/16 x 12/16) or correct} / {their (4/16 x 12/16) + (their (12/16 x 4/15) from part(a) or 0.7375 or 59/80 or correct} seen as the denominator of a single fraction.
5. [A1] 0.254237... to at least 3 SF. If one or more M not scored SCB1 for 15/59 ,0.254237... to at least 4 SF WWW.