Tree Diagrams: Eduqas GCSE Foundation November 2024 Paper 1 Q24

Foundation November 2024 Paper 1 Q24

EduqasFoundationCurrent spec7 marksTree Diagrams

24. Hannah and Imran often play badminton and tennis matches against each other.

The probability that Hannah wins a badminton match is \(\dfrac{9}{10}\).

The probability that Hannah wins both a badminton match and a tennis match is \(\dfrac{9}{50}\).

One Saturday, Hannah and Imran play one badminton match and one tennis match.
The outcomes of the matches are independent.

(a) Complete the tree diagram below. [4]

(b) Calculate the probability that Hannah wins exactly one match. [3]

Mark scheme (a)

Scheme	Marks	Comments
\(\dfrac{9}{10}\) and \(\dfrac{1}{10}\) oe, correctly placed on the tree diagram	B1	Allow equivalent decimal probabilities
\(\frac{9}{50} \div \frac{9}{10}\) or \(\frac{9}{10} \times x = \frac{9}{50}\)	M1
\(\dfrac{1}{5}\) oe	A1	Implies M1
\(\dfrac{1}{5}\), \(\dfrac{4}{5}\) and \(\dfrac{1}{5}\), \(\dfrac{4}{5}\) oe on tennis branches	B1	FT provided M1 awarded AND ‘their \(\dfrac{1}{5}\) and \(\dfrac{4}{5}\)’ add to 1

Mark scheme (b)

Scheme	Marks	Comments
\(\left(\frac{9}{10} \times \frac{4}{5}\right) + \left(\frac{1}{10} \times \frac{1}{5}\right)\) oe	M2	FT ‘their \(\dfrac{1}{5}\) and \(\dfrac{4}{5}\)’ provided they add to 1 M1 for sight of \(\frac{9}{10} \times \frac{4}{5}\) or \(\frac{1}{10} \times \frac{1}{5}\) oe
\(\dfrac{37}{50}\) oe	A1
	(7)