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 supermarket recorded the $300$ customers who used the self-service tills one morning. The two-way table shows how each customer paid and whether they needed help from an assistant.
Card Cash Phone Total
Needed help $21$ $18$ $9$ $48$
Did not need help $129$ $42$ $81$ $252$
Total $150$ $60$ $90$ $300$
(a) One of the customers who paid by cash is chosen at random.

Work out the probability that this customer needed help.

(b) One of the customers who needed help is chosen at random.

Work out the probability that this customer did not pay by cash.

(c) One of the customers who paid by card or by phone is chosen at random.

Work out the probability that this customer needed help.
Level 5 · 8 marksTry it
2
A gym has $400$ members. Every member is on either the standard plan or the premium plan, and $240$ of the members are on the standard plan.

Given that a member is on the premium plan, the probability that they attend a class is $0.65$ .

Altogether $250$ of the $400$ members attend a class.

(a) Work out the number of premium members who attend a class.

(b) One of the members who attends a class is chosen at random.

Work out the probability that this member is on the standard plan.

(c) One of the members who does not attend a class is chosen at random.

Work out the probability that this member is on the premium plan.
Level 5 · 8 marksTry it

	Card	Cash	Phone	Total
Needed help	$21$	$18$	$9$	$48$
Did not need help	$129$	$42$	$81$	$252$
Total	$150$	$60$	$90$	$300$