Conditional probability

When do we use conditional probability?

Likelihood of an event occurring if that another event has already happened.

Formula:

P(A|B) = P(A and B)/P(B)

• P(A|B) - the probability of A given B.
• P(A and B) - the probability of A and B.
• P(B) - the probability of B.

Task example:

You have 25 balls: 20 **yellow and 5 blue. Among these balls, 5 yellow balls have a defect and 4 blue. The randomly selected ball is blue; calculate the probability that it has a defect.

P(A|B) = P(A and B)/P(B)

• P(deffect and blue) = 4/25 = 0.16 = 16%.
• P(blue) = 5/25 = 0.2 = 20%.
• P(deffect|blue) = 16%/20% = 80%.