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 %

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