Box A contains 6 green balls and 3 yellow balls. Box B contains 4 green balls and x yellow balls. A ball is chosen at random from box A and placed in box B. A ball is then chosen at random from box B.

Mark scheme

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

1. [B1] Correct structure and probabilities for Box A branches.
2. [B1] Completely correct structure and one correct probability for a Box B branch including label for G or Y.
3. [B1] Completely correct structure and second correct probability on a Box B branch including label G or Y.
4. [B1] Completely correct structure and remaining two probabilities correct on Box B branches, including labels for G or Y. SC B1 if correct shape diagram but only four correct algebraic probs for GG, GY, YG and YY.
5. [M1] P(GG) + P(YY) = (6/9)*(5/(5+x)) + (3/9)*( (x+1)/(5+x) ) (or) x their (5+x+or their (1+x))
6. [M1] 15(x+11) = 24(x+5) OE Accept sum of their products equated to 8/15 and rearranged to form a linear equation.
7. [A1] Solve: x = 5