Question

among 21 - to 25 - year - olds, 29.2% say they have driven while under the influence of alcohol. suppose that five 21 - to 25 - year - olds are selected at random. complete parts (a) through (d)
(a) what is the probability that all five have driven while under the influence of alcohol?
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the probability of a single person

The probability \(p\) that a 21 - to 25 - year - old has driven while under the influence of alcohol is \(p = 0.292\).

Step2: Use the multiplication rule for independent events

Since the selections are independent, the probability that all \(n = 5\) have driven while under the influence is \(P(X = 5)=p\times p\times p\times p\times p=p^{n}\).
Substitute \(p = 0.292\) and \(n = 5\) into the formula: \(P(X = 5)=(0.292)^{5}\).
Calculate \((0.292)^{5}=0.292\times0.292\times0.292\times0.292\times0.292\approx0.0021\)

Answer:

\(0.0021\)