Question

Among 34​- to 39​-year-olds, 41​% say they have danced in public while under the influence of alcohol. Suppose five 34​- to 39​-year-olds are selected at random. Complete parts​ (a) through​ (d) below. ​(a) What is the probability that all five have danced in public while under the influence of  alcohol​? ​(Round to four decimal places as​ needed.) ​(b) What is the probability that at least one has not danced in public while under the influence of alcohol​? ​(Round to four decimal places as​ needed.) ​(c) What is the probability that none of the five have danced in public while under the influence of alcohol​? ​(Round to four decimal places as​ needed.) ​(d) What is the probability that at least one has danced in public while under the influence of alcohol​? ​(Round to four decimal places as​ needed.)

Answer 1

n = 5,

Probability of dancing in public under alcohol influence, p = 0.41

Probability of not dancing in public under alcohol influence, q = 1-p = 0.41

​(a) probability that all five have danced in public while under the influence of alcohol​, P(X = 5) =

= 5!/(5!* 0!) * 0.41^5 * 0.59^0

= 0.0116

(b) probability that at least one has not danced in public while under the influence of alcohol, P(X ≥ 1) ​ = 1 - P(X<1)

= 1 - 5!/(0!* 5!) * 0.59^0 * 0.41^5

= 1 - 0.0116 = 0.9884

​(c) probability that none of the five have danced in public while under the influence of alcohol​, P(X = 0) =

= 5!/(0!* 5!) * 0.41^0 * 0.59^5

= 0.0715

(d) probability that at least one has danced in public while under the influence of alcohol​, P(X ≥ 1) =

= 1 - P(X = 0)

= 1 - 0.0715 = 0.9285