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

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