The probability that Nikita wins a tennis match depends on the surface of the tennis court on which she is playing. The probability that she plays on a grass court is \(0.4\). The probability that Nikita wins on a grass court is \(0.35\). The probability that Nikita wins when the court is not grass is \(0.25\).

Complete the following tree diagram.

Find the probability that Nikita wins a match.

              (A1)(A1)(A1)    (C3)

Note: Award (A1) for each correct entry.

[3 marks]

\(0.4 \times 0.35 + 0.6 \times 0.25\)        (A1)(ft)(M1)

Note: Award (A1)(ft) for two correct products from their tree diagram seen, and (M1) for the addition of their products.

\( = 0.29\)        (A1)(ft)   (C3)

Note: Follow through from part (a).

[3 marks]

Question 1: Tree diagram
This was a good starting question and answered correctly by the majority of the candidates. However, some candidates were unable to interpret part (b). The weakest seemed not to be aware that the sum of the probabilities on the branches should equal 1.

Question 1: Tree diagram
This was a good starting question and answered correctly by the majority of the candidates. However, some candidates were unable to interpret part (b). The weakest seemed not to be aware that the sum of the probabilities on the branches should equal 1.