A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2018 · Q37 Marks

A box contains 3 red balls and 5 blue balls. One ball is taken at random from the box and not replaced. A yellow ball is then put into the box. A second ball is now taken at random from the box.

(i)Complete the tree diagram to show all the outcomes and the probability for each branch.[2]
(ii)Find the probability that the two balls taken are the same colour.[2]
(iii)Find the probability that the first ball taken is red, given that the second ball taken is blue.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Fully correct labelled tree and correct probabilities for 'First Ball'
[B1] Correct probabilities (with corresponding labels) for 'Second Ball'
[M1] Correct unsimplified expression from their tree diagram, Σp = 1 on each branch
[A1] Correct answer (13/32 (0.406))
[M1] P(1st ball red)×P(2nd ball blue) from their tree diagram seen unsimplified as numerator or denominator of a fraction Allow Σp ≠ 1 on each branch
[M1] Correct unsimplified expression for P(B) from their tree diagram seen as denominator of a fraction. Allow Σp ≠ 1 on each branch
[A1] Correct answer (3/7 (0.429))

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