GCSE · Combined events & tree diagrams

Tree diagrams & independent eventsExam-style questions

Building a tree from a worded scenario, and why you multiply along a branch and add between branches — plus the branches-sum-to-1 check and the "at least one" complement that turns seven calculations into one.

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

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A bag contains $3$ red counters and $2$ blue counters.

A counter is taken at random and replaced. A second counter is then taken at random.

Work out the probability that the two counters are different colours. (3 marks)
Level 3 · 3 marksTry it
2
The probability that Sam is late for school on any given day is $0.15$

Whether Sam is late on one day is independent of whether he is late on any other day.
(a) Work out the probability that Sam is late on both of the next two days. (2 marks)
(b) Work out the probability that Sam is late on exactly one of the next two days. (2 marks)
Level 3 · 4 marksTry it
3
Bea rolls a fair six-sided dice numbered $1$ to $6$ . She also spins a spinner with $5$ equal sections, $2$ of which are green.

The roll of the dice and the spin of the spinner are independent.

(a) Work out the probability that the dice lands on $6$ and the spinner lands on green.

(b) Work out the probability that the dice does not land on $6$ and the spinner does not land on green.
Level 3 · 5 marksTry it
4
The probability that Nia's train is on time on any morning is $0.85$ . Whether the train is on time on one morning is independent of every other morning.

Nia catches the train on Monday morning and on Tuesday morning.

(a) Work out the probability that the train is on time on both mornings.

(b) Work out the probability that the train is on time on exactly one of the two mornings.
Level 3 · 5 marksTry it