GCSE Maths revision · Higher: probability and statistics

Algebraic probability

Higher only

The idea

When probabilities are written in terms of $x$ , use the fact that they add to $1$ , or the given total probability, to form an equation in $x$ , then solve it.

Write each probability in terms of $x$ .
Form an equation: all outcomes add to $1$ , or a product along branches equals the given value.
Solve, and reject any value that gives a probability outside $0$ to $1$ .

Watch out Multiply along a branch using each probability given what came before it.

See it worked

Worked exampleNon-calculator3 marks

An experiment has exactly four possible outcomes A, B, C and D. Their probabilities are 2x, 3x, x + 0.1 and 0.3 respectively. Work out the probability of outcome B.

$2x+3x+x+0.1+0.3=1$
$6x=0.6$
The probabilities add to 1: 2x + 3x + x + 0.1 + 0.3 = 1.
Therefore 6x = 0.6, so x = 0.1.
P(B) = 3x = 0.3.

Answer 0.3

Your turn

Question 1Non-calculator3 marks

$P(A) = 0.4$ , $P(B) = 0.5$ and $P(A \cap B) = 0.2$ .

(a) Are $A$ and $B$ independent? You must show how you get your answer.

(b) Work out $P(A \cup B)$ .

Question 2Non-calculator5 marks

A bag contains $x$ red counters and 5 blue counters, and there are more blue counters than red. Two counters are taken at random without replacement. The probability that they are different colours is $\frac{5}{9}$ .

Work out the value of $x$ .

Question 3Non-calculator3 marks

A bag contains n red counters and 4 blue counters, where n is greater than 4. Two counters are selected at random without replacement. The probability that the counters are different colours is 8/15. Work out n. You must show your working.

In past papers

16 official questions in 16 papers since 2019. The latest:

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