GCSE · Combined events & tree diagrams

Conditional probabilityExam-style questions

Why "given that" shrinks the sample space to the group you were told about, so the denominator becomes that group's total — and why P(A given B) and P(B given A) are two different questions with two different answers.

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8 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The two-way table shows information about the $80$ members of a swimming club.
Under 16 16 or over Total
Male $18$ $22$ $40$
Female $27$ $13$ $40$
Total $45$ $35$ $80$
(a) One of the members aged under 16 is chosen at random.

Work out the probability that this member is female.

(b) One of the female members is chosen at random.

Work out the probability that this member is aged under 16.
Level 2 · 4 marksTry it
2
A cycling club has $120$ members. $45$ of the members are aged under $18$ and the rest are aged $18$ or over.

$27$ of the members aged under $18$ own a racing bike.

$30$ of the members aged $18$ or over own a racing bike.

(a) One of the members aged under $18$ is chosen at random.

Work out the probability that this member owns a racing bike.

(b) One of the members who owns a racing bike is chosen at random.

Work out the probability that this member is aged $18$ or over.
Level 3 · 5 marksTry it
3
The two-way table gives information about how the $150$ pupils in Years 10 and 11 travel to school. One cell has not been filled in.
Walk Cycle Bus Total
Year 10 $24$ $15$ $36$ $75$
Year 11 $31$ $9$ $75$
Total $55$ $24$ $71$ $150$
(a) Work out the number of Year 11 pupils who travel by bus.

(b) One of the Year 11 pupils is chosen at random.

Work out the probability that this pupil cycles to school.

(c) One of the pupils who cycles to school is chosen at random.

Work out the probability that this pupil is in Year 10.
Level 3 · 5 marksTry it
4
$400$ adults in a town were asked whether they hold a driving licence and whether they own a car. The two-way table shows the results.
Owns a car Does not own a car Total
Holds a licence $210$ $70$ $280$
Does not hold a licence $14$ $106$ $120$
Total $224$ $176$ $400$
(a) One of the $400$ adults is chosen at random.

Work out the probability that this adult owns a car and holds a licence.

(b) One of the adults who owns a car is chosen at random.

Work out the probability that this adult holds a licence.

(c) One of the adults who holds a licence is chosen at random.

Work out the probability that this adult owns a car.
Level 3 · 6 marksTry it
5
A theatre sold $240$ tickets for a play. $90$ of the tickets were sold online and the rest were sold at the box office.

Every ticket was either a concession ticket or a full-price ticket. Altogether $44$ of the $240$ tickets were concession tickets.

Given that a ticket was sold online, the probability that it was a concession ticket is $\frac{2}{15}$ .

(a) Work out the number of concession tickets that were sold online.

(b) One of the concession tickets is chosen at random.

Work out the probability that it was sold at the box office.
Level 4 · 5 marksTry it

	Under 16	16 or over	Total
Male	$18$	$22$	$40$
Female	$27$	$13$	$40$
Total	$45$	$35$	$80$

	Walk	Cycle	Bus	Total
Year 10	$24$	$15$	$36$	$75$
Year 11	$31$	$9$		$75$
Total	$55$	$24$	$71$	$150$

	Owns a car	Does not own a car	Total
Holds a licence	$210$	$70$	$280$
Does not hold a licence	$14$	$106$	$120$
Total	$224$	$176$	$400$

3 more questions on conditional probability

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