A California municipal court district assembles a panel of 4

A California municipal court district assembles a panel of 45 persons; they are to be available to serve as jurors for trials scheduled during a three-week period. When a trial is scheduled, an initial collection of 18 of these persons will be selected at random from the panel of 45 for questioning by the judge and the attorneys for the two sides of the case.

(a) If you are one of the 45 persons on the panel, what is the probability that you will be among the initial 18 selected? (b) Suppose both you and your neighbor are on the panel; what is the probability that at least one of you two will be included in the initial selection?

Solution

a) P( will be among the initial 18 selected ) = 1 * 44 C 17 / 45 C 18 = 0.4

b)
P(atleast one of use selected) = 2 C 1 * 43 C 17 / 45 C 18 = 0.4909