Among 53- 58 year olds, 41% say they have driven a car while under the influence...

Among 53- 58 year olds, 41% say they have driven a car while under the influence of alcohol. Suppose six 53 to 58 year olds are selected at random. Complete parts (a) through (d) below.

A.) what is the probability that all six have driven a car while under the influence of alcohol?

___ (Round to four decimal places as needed).

B.) what is the probability that at least one has not driven a car while under the influence of alcohol? Round to four decimal places as needed).

C.) What is the probability that none of the six have driven a car while under the influence of alcohol? Round to four decimal places as needed).

D.) What is the probability that at least one has driven a car while under the influence of alcohol? Round to four decimal places as needed).

Expert Solution

P(driven a car while under the influence of alcohol) = 0.41

n = 6

a) P(X = 6) = 0.41⁶ = 0.0048

b) P(at least one has not driven a car while under the influence of alcohol) = 1 - P(all of them have driven a car while under the influence of alcohol)

= 1 - (0.41)⁶

= 0.9952

c) P(none of the 6 have driven a car while under the influence of alcohol) = (1 - 0.41)⁶ = 0.0422

d) P(at least one has driven a car while under the influence of alcohol) = 1 - P(none of the 6 have driven a car while under the influence of alcohol) = 1 - 0.0422 = 0.9578

orchestra answered 2 years ago

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