In a small city approximately 18 of those eligible are calle

In a small city, approximately 18% of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year.

(a) What is the probability that a particular eligible person in this city is selected in both of the next 2 years? (Enter your answer to four decimal places.)


(b) What is the probability that a particular eligible person in this city is selected in all three of the next 3 years? (Enter your answer to six decimal places.)

Solution

18% of the population are selected. If the population size is N and the number of selected people is n then,

n/N * 100=18

i.e., n/N=0.18

Thus, probability of selecting a person out of N distinct persons in \"n\" draws is n/N = 0.18

So, P(a person is selected in a particular year)=0.18

(a)

P(a person is selected in 2 consecutive years)

=P(a person is selected in year 1) * P(the person is selected in year 2)

=0.18 * 0.18

=0.0324

(b)

P(a person is selected in 3 consecutive years)=0.18*0.18*0.18

=0.005832