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 \frac{4}{35} \frac{18}{35} \frac{12}{35} \frac{1}{35}

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

E (x) = x1p1 + x2p2+……..+xnpn.

Here, x can take on the values 0, 1,2 or 3, with probabilities \frac{4}{35} \frac{18}{35} \frac{12}{35} and \frac{1}{35} respectively.

E(x) = 0* \frac{4}{35}  1*\frac{18}{35} 2*\frac{12}{35}3* \frac{1}{35}

=1.29

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

 

 

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