Higher June 2023 Paper 1R Q13

EdexcelHigherCurrent spec3 marksTree Diagrams

13 Novak is going to play two games of tennis.

The probability that he wins the first game is 0.7

If he wins the first game, the probability that he wins the second game is 0.9
If he loses the first game, the probability that he wins the second game is 0.4

(a) Complete the probability tree diagram. (1)

Probability tree diagram. First game: Novak wins 0.7, Novak loses 0.3. Second game after a win: Novak wins 0.9, Novak loses blank. Second game after a loss: Novak wins 0.4, Novak loses blank

(b) Work out the probability that Novak wins both games of tennis. (2)

Scheme	Marks
0.1 and 0.6	B1
	(1)

Mark scheme (b)

Scheme	Marks
0.7 × 0.9 or 1 − (0.7 × “0.1” + 0.3 × 0.4 + 0.3 × “0.6”)	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: 0.63	A1
	(2)
	(3 marks)

Notes

M1: must be considering one correct product only or 1 − (all 3 correct products only)
allow ft if using
1 − P(WL or LW or LL)

A1: oe eg 63% or \(\dfrac{63}{100}\)

allow ft if using

1 − P(WL or LW or LL)