The probability of any person in your Student Council being

The probability of any person in your Student Council being selected for the Spring Dance committee is 0.3, and the probability that a person on the Spring Dance Committee is Problem 2: elected Chairperson of this committee is 0.2. Find the probability that a member of the Student Council, chosen at random, is the Chairperson of the committee.

Solution

Here we are given that the probability that a student is selected for the spring dance commettee is given as:

P( spring dance committee ) = 0.3

Also given that he is in spring dance committee, probability that he is selected as the chairperson of the committee is given as:

P( chairperson | spring dance committee ) = 0.2

Using bayes theorem, we get:

P( chairperson and the spring dance commiteee ) = P( chairperson | spring dance committee ) P( spring dance committee )

P( chairperson and the spring dance commiteee ) = 0.3*0.2 = 0.06

Therefore the probability that a member of the student council, chosen at random is the chairperson of the committee is given as 0.06