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 a particular eligible person in this city is selected two years in a row? three years in a row?

Short answer

The probability that an eligible person is selected for jury duty two years in a row is \(0.0225\) and three years in a row is \(0.003375\).

Step-by-step solution

Understand the given situation and the probability for each independent event

The probability of a person being called for jury duty in a particular year is \(15\%\) or \(0.15\). Given that the individual cannot be called more than once in the same year, each year's selection is an independent event.

Apply the multiplication rule for independent events for two years

The probability of two independent events A and B happening is given by P(A and B) = P(A) * P(B). In this case, both probabilities are \(0.15\). So, P(person selected two years in a row) = P(selected in first year) * P(selected in the second year) = \(0.15 * 0.15 = 0.0225\).

Apply the multiplication rule for independent events for three years

The same rule can be applied for three years. So, P(person selected three years in a row) = P(selected in first year) * P(selected in the second year) * P(selected in the third year) = \(0.15 * 0.15 * 0.15 = 0.003375\).