In a small city approximately 11 of those eligible are calle

In a small city, approximately 11% 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

The probability of getting selected as a jury is p=0.11. Now let us assume that the event of being selected in one year and in another year are independent of each other.

Let A=an eligible person getting selected in year 1

B=an eligible person getting selected in year 2

C=an eligible person getting selected in year 3.

As per our assumption we have A B C as independent events.

Hence

P(Getting Selected in both of the next 2 years)= P( A and B)=P(A)P(B) [as they are indpendent]=0.11^2=.0121

P(Getting Selected in both of the next 3years)= P( A and B and C)=P(A)P(B) P(C)[as they are indpendent]=0.11^3=.001331