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 coin is biased so that it is twice as likely to land on heads as to land on tails.

Femi throws the coin $n$ times, where $n \geqslant 2$

Write down an expression, in terms of $n$ , for the probability that Femi's $n$ throws include at least one head and at least one tail.

(2 marks)
Level 5 · 2 marksTry it
2
A machine makes components. The probability that any component it makes is faulty is $0.04$ , independently of every other component.

An inspector takes a sample of $3$ components at random from a large batch.

(a) Work out the probability that at least one of the $3$ components in the sample is faulty. Give your answer correct to $3$ decimal places.

(b) The inspector takes $500$ such samples of $3$ components. Work out an estimate for the number of these $500$ samples that contain at least one faulty component.
Level 5 · 5 marksTry it
3
Each time Salma takes a shot at a basketball hoop, the probability that she scores is $p$ . The results of her shots are independent.

Salma takes two shots. The probability that she misses both shots is $0.09$ .

(a) Work out the value of $p$ .

(b) Work out the probability that Salma scores with exactly one of her two shots.
Level 5 · 6 marksTry it