GCSE-ready- Home
- Lessons
- GCSE & IGCSE Mathematics
- Conditional probability
Conditional probability
Conditional probability asks: given that one thing has happened, how likely is another?
Notation
P(B | A) means the probability of B given A has happened.
P(B | A) = P(A and B)P(A)
P(B | A) = P(A and B)P(A)
From a two-way table
Restrict to the row or column you are given, then find the fraction.
Of 60 students, 25 are in Year 10, and 15 of those walk to school. P(walks | Year 10) = 1525.
Of 60 students, 25 are in Year 10, and 15 of those walk to school. P(walks | Year 10) = 1525.
Independence check
A and B are independent if P(A and B) = P(A) × P(B), or if P(B | A) = P(B).
P(A) = 0.5 and P(A and B) = 0.2. Find P(B | A).
- P(B | A) = 0.20.5
Answer: 0.4
Given means restrict the total to what is given. P(B | A) = P(A and B) ÷ P(A). Independence means P(A and B) = P(A) × P(B).
Check you have got it
Answer 6 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.