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. What is the probability that an eligible person in this city is selected in both of the next 2 years? All of the next 3 years?

Short answer

The probability that an eligible person in this city is selected for jury duty in both of the next 2 years is approximately \(2.25%\), and in all of the next 3 years is approximately \(0.3375%\).

Step-by-step solution

Identify the probability of the event

The exercise gives us the probability of an individual being called for jury duty in any given year, which is \(15%\). We can express this as a decimal, \(0.15\), for calculation purposes.

Calculate the probability over two years

Since the events are independent, we can calculate the compound probability over two years by multiplying the individual probabilities together. Therefore, the probability of being selected for jury duty both years is \(0.15 * 0.15 = 0.0225\) or \(2.25%\).

Calculate the probability over three years

Similarly, we can calculate the probability over three years by multiplying the individual probabilities for each year. Therefore, the probability of being selected for jury duty in all three years is \(0.15 * 0.15 * 0.15 = 0.003375\) or \(0.3375%\).