Conditional Probability (Edexcel GCSE Maths) : Revision Note

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)

  • It is written

    • Pronounced "the probability of A given 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) =

    • 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) =

    • 1 possibility (6) out of only 4 possibilities (2, 4, 6, 8)

    • This is a conditional probability, written P(multiple of 3 | even) =