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 0.0021
(round to four decimal places as needed.)
(b) what is the probability that at least one has not driven while under the influence of alcohol?
the probability is 0.9979
(round to four decimal places as needed.)
(c) what is the probability that none of the five have driven while under the influence of alcohol?
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the probability of not driving under influence

The probability of driving under influence \(p = 0.292\). So the probability of not driving under influence \(q=1 - p=1 - 0.292 = 0.708\)

Step2: Use the multiplication rule for independent events

Since the five people are selected at random (independent events), the probability that none of the five have driven under influence is \(q\times q\times q\times q\times q=q^{5}\)
Substitute \(q = 0.708\) into the formula: \(0.708^{5}\)

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Answer:

\(0.1777\)