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
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
2
The two-way table shows information about $200$ people who work in an office and how they travel to work.
Cycles to work Does not cycle to work Total
Aged under 30 $24$ $56$ $80$
Aged 30 or over $36$ $84$ $120$
Total $60$ $140$ $200$
(a) One of the $200$ people is chosen at random.

Write down the probability that this person cycles to work.

(b) One of the people aged under $30$ is chosen at random.

Work out the probability that this person cycles to work.

(c) Ellie says that whether a person cycles to work is independent of their age group.

Is Ellie correct? You must justify your answer.
Level 4 · 5 marksTry it

	Cycles to work	Does not cycle to work	Total
Aged under 30	$24$	$56$	$80$
Aged 30 or over	$36$	$84$	$120$
Total	$60$	$140$	$200$