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.
8 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try
- 1A cycling club has members. of the members are aged under and the rest are aged or over.
of the members aged under own a racing bike.
of the members aged or over own a racing bike.
(a) One of the members aged under 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 or over.Level 3 · 5 marksTry it - 2The two-way table gives information about how the pupils in Years 10 and 11 travel to school. One cell has not been filled in.
(a) Work out the number of Year 11 pupils who travel by bus.Walk Cycle Bus Total Year 10 Year 11 Total
(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 - 3adults in a town were asked whether they hold a driving licence and whether they own a car. The two-way table shows the results.
(a) One of the adults is chosen at random.Owns a car Does not own a car Total Holds a licence Does not hold a licence Total
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