Problem 1029

A committee of 3 members is selected from a club made up of 3 junior members and 4 senior members. What is the expected number of juniors in the committee?

 

Solution:-

 

To find the expected number of juniors, we need to find the expected value of the number of juniors. For this, we can construct a table for the random variable x, where x is the number of junior in the 3 person committee.

Number of Juniors 0 1 2 3

Probability

Next, find the expected value. If the random variable x can take on n values, x₁,x₂,……..x_n, with probabilities, p₁, p₂,……p_n respectively, than the expected values is

E (x) = x₁p₁ + x₂p₂+……..+x_np_n.

Here, x can take on the values 0, 1,2 or 3, with probabilities respectively.

E(x) =

=1.29

Thus, the number of expected juniors on the committee is about 1.29.