A-LevelMathematicsProbability and statistics9709/61 · May/June 2017 · Q36 Marks

Redbury United soccer team play a match every week. Each match can be won, drawn or lost. At the beginning of the soccer season the probability that Redbury United win their first match is 1/3, with equal probabilities of losing or drawing. If they win the first match, the probability that they win the second match is 7/10 and the probability that they lose the second match is 1/10. If they draw the first match they are equally likely to win, draw or lose the second match. If they lose the first match, the probability that they win the second match is 3/10 and the probability that they draw the second match is 1/20.

(i)Draw a fully labelled tree diagram to represent the first two matches played by Redbury United in the soccer season.[2]
(ii)Given that Redbury United win the second match, find the probability that they lose the first match.[4]

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 (May/June 2017). The mark or mark type is shown in brackets.

[M1] Correct shape i.e. 3 branches then 3 by 3 branches, labelled and clear annotation Condone omission of lines for first match result providing the probabilities are there.
[A1] All correct probs with fully correct shape and probs either fractions or decimals not 1.5/5 etc.
[M1] Attempt at P(L1∩W2) as a two-factor prod only as num or denom of a fraction
[M1] Attempt at P(W2) as sum of appropriate 3 two-factor probs OE seen anywhere
[A1] Unsimplified correct P(W2) num or denom of a fraction
[A1]

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