Multiple Events: Eduqas GCSE Higher November 2024 Paper 1 Q7

Higher November 2024 Paper 1 Q7

EduqasHigherCurrent spec7 marksMultiple Events Tree Diagrams

7. 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
\(\frac{9}{10}\) and \(\frac{1}{10}\) 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
\(\frac{1}{5}\) oe	A1	Implies M1
\(\frac{1}{5}\), \(\frac{4}{5}\) and \(\frac{1}{5}\), \(\frac{4}{5}\) oe on tennis branches	B1	FT provided M1 awarded AND ‘their \(\frac{1}{5}\) and \(\frac{4}{5}\)’ 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 \(\frac{1}{5}\) and \(\frac{4}{5}\)’ 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
\(\frac{37}{50}\) oe	A1
	(7)