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?




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}


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



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