Conditional Probability (Edexcel IGCSE Maths)

Spec point — 6.3B

Conditional probability

What is a conditional probability?

• A conditional probability is the probability of something happening (A) given that something else has already happened (B)

How do I calculate conditional probabilities?

• Conditional probabilities must be out of a smaller restricted set of outcomes (not out of all possible events)

  • For example, if a computer randomly selects a digit from 1, 2, 3, 4, 5, 6, 7, 8, 9

    • P(it select a multiple of three) = $\frac{3}{9}$
    • This is not a conditional probability
    • There are 3 possibilities (3, 6, 9) out of all 9 possibilities

  • However, if you program the computer to only select from even numbers, then

    • P(it selects a multiple of three given that it selects an even number) = $\frac{1}{4}$
    • 1 possibility (6) out of only 4 possibilities (2, 4, 6, 8)
    • This is a conditional probability

Exam Hint Look out for conditional probability questions within larger questions on two-way tables, Venn diagrams or tree diagrams.

They often use the phrase "given that".

Worked Example A Venn diagram is shown below. The numbers represent numbers of people.

When one random person is selected, find the probability that they are in set $A$given that they are in set $B$, simplifying your answer.

Answer:

*Given that B is true, your probability will be out of the total number in *B

Find the total number in* B*

63 + 42 = 105

Out of this total number in B, find how many are in A

42

Form a probability by dividing 42 by 105

straight P (A given B)=42 / 105

Simplify your answer

straight P (A given B)=2 / 5