Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

Every week, the Redbury United soccer team takes part in one match. Each match results in a win, a draw or a loss. At the beginning of the soccer season, the probability that Redbury United win their first match is $\frac{3}{5}$, and the probabilities of losing or drawing are equal. If they win the first match, the probability that they win the second match is $\frac{7}{10}$ and the probability that they lose the second match is $\frac{1}{10}$. 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 $\frac{3}{10}$ and the probability that they draw the second match is $\frac{1}{20}$.
(i)[2]

Draw a fully labelled tree diagram showing the first two matches played by Redbury United in the soccer season.

(ii)[4]

Given that Redbury United win the second match, find the probability that they lose the first match.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct probability tree layout with three branches and then three branches, all labelled

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