In a small city, approximately 15% of those eligible are called for jury duty in
ID: 3307165 • Letter: I
Question
In a small city, approximately 15% 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?
b) What is the probability that a particular eligible person in this city is selected in all three of the next 3 years?
c) What is the probability that a particular eligible person in this city is not selected in all three of the next 3 years?
d) What is the probability that a particular eligible person in this city is selected at least one in the next 3 years?
e) Are the events of a particular person in this city being selected each year independent?
Explanation / Answer
Probability of a person being eligible = 0.15
Probability of a person not being eligible = 1 - 0.15 = 0.85
a) Probability that a particular eligible person is selected in both of the next 2 years = 0.15 * 0.15 = 0.0225.
b) Probability that a particular eligible person is selected in all 3 of the next 3 years = 0.15 * 0.15 * 0.15 = 0.003375.
c) Note: This question has two meanings.
If the question asks to find probability that the person is not selected in all three years i.e there is atleast one year where he is not selected, the answer is 1 - 0.003375 = 0.996625.
If the question asks to find probability that the person is not selected in all three years i.e he is not selecte in any year, the answer is 0.85 * 0.85 * 0.85 = 0.614125.
d) The probability that the person is selected in atleast one of the 3 years = 1 - 0.614125 = 0.385875.
e) Since the people are selected at random and the outcome of one does not depend on another, the events are independent.