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 has $3$ red and $2$ blue counters. A counter is taken, its colour noted, and it is put back. A second counter is taken. Write down the probability that the second counter is blue.
Level 1 · 1 markTry it
2
The probability that Ana is late on any day is $0.2$ , independently of other days. Work out the probability that she is late on both Monday and Tuesday.
Level 1 · 1 markTry it
3
A fair coin is flipped twice. Use a tree diagram or a list to find the probability of getting a head then a tail.
Level 1 · 2 marksTry it
4
Two events $A$ and $B$ are independent. $P(A) = 0.3$ and $P(B) = 0.6$ .

(a) Work out the probability that both $A$ and $B$ happen. [1]

(b) Work out the probability that neither $A$ nor $B$ happens. [2]
Level 2 · 3 marksTry it
5
Each time Ravi plays a game on his phone, the probability that he wins is $0.4$ .

Ravi plays the game twice. The results of the two games are independent.

(a) Work out the probability that Ravi wins both games.

(b) Work out the probability that Ravi loses both games.
Level 2 · 4 marksTry it

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