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 fair spinner has $6$ equal sections.

$4$ of the sections are red and the other $2$ sections are blue.

Ayla spins the spinner $3$ times.

Show that the probability that the spinner lands on red at least twice is $\frac{20}{27}$

(4 marks)
Level 4 · 4 marksTry it
2
A spinner can land on red, blue or yellow.

$P(\text{red}) = 0.5$ and $P(\text{blue}) = 0.2$ .

The spinner is spun twice. The two spins are independent.

(a) Work out the probability that the spinner lands on yellow on any one spin.

(b) Work out the probability that the spinner lands on the same colour on both spins.
Level 4 · 4 marksTry it
3
A bag contains $3$ red counters and $7$ white counters.

A counter is taken at random from the bag, its colour is recorded, and the counter is put back in the bag. This is done three times.

(a) Work out the probability that all three counters taken are red.

(b) Work out the probability that exactly two of the three counters taken are red.
Level 4 · 5 marksTry it
4
On any day, the probability that it rains in a town is $0.2$ . Whether it rains on one day is independent of whether it rains on any other day.

Kofi wants the probability that it rains on at least one of the next two days. He writes:

$P(\text{at least one rainy day}) = 0.2 + 0.2 = 0.4$

(a) Explain why Kofi's method is wrong.

(b) Work out the correct probability that it rains on at least one of the next two days.
Level 4 · 4 marksTry it