A-level · Probability

Conditional probability and tree diagramsExam-style questions

Using tree diagrams where the second-stage branches are conditional probabilities — multiplying along branches for P(A ∩ B), adding the paths to an event, and reversing the condition to find P(first | second).

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19 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Niamh and Isla play a tennis match. The match is decided over the best of three sets: it ends as soon as one player has won two sets.
- Niamh wins the first set with probability $0.6$ .
- In every later set, the player who won the previous set wins with probability $0.7$ .
The tree diagram below shows the possible results of the first set.(a) State the greatest number of sets that can be played in the match.

(1 mark)
(b) Complete the tree diagram to show all the possible results of the match, writing the probability on each branch.

(3 marks)
(c) Determine the probability that the match is won by Isla.

(3 marks)
(d) Determine the probability that the match goes to a third set.

(2 marks)
(e) Determine the probability that the match is won by Isla, given that it goes to a third set.

(4 marks)
Level 5 · 13 marksTry it