Conditional Probability Formula

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

Question 1:

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?

Solution:

The formula of Conditional probability Formula is:

P (B|A) = P(A ∩ B)⁄P(A)

P(Absent | Friday)= P (Absent and Friday)⁄P(Friday)

= 0.030.2

= 0.15

= 15 %


Practise This Question

The time taken to travel 30 km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11 km then the total time taken is 11 hours more than earlier. Find the speed of the stream.