Conditional probability formula gives the measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, “the conditional probability of A given B”, or “the probability of A under the condition B”. The events are usually written as P(A|B), or sometimes P B(A). The formula for conditional probability for both the conditions i.e. “the probability of A under the condition B” and “the probability of B under the condition A” are stated below.
Formula for Conditional Probability
|Conditional Probability of A given B||
P (A|B) = P(A ∩ B)⁄P(A)
|Conditional Probability of B given A||P (B|A) = P(B ∩ A)⁄P(B)|
Solved Examples Using Conditional Probability Formula
The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?
The formula of Conditional probability Formula is:
P (B|A) = P(A ∩ B)⁄P(A)
P(Absent | Friday)= P (Absent and Friday)⁄P(Friday)
= 15 %