Question

Among 46​- to 51​-year-olds, 28​% say they have called a talk show while under the influence of peer pressurepeer pressure. Suppose sevenseven 46​- to 51​-year-olds are selected at random. ​(a) What is the probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressurepeer pressure​? ​(b) What is the probability that at least one has called nbspcalled a talk showa talk show while under the influence of peer pressurepeer pressure​?

Answer 1

0.8997, 0.9999

Explanation:

Given that among 46​- to 51​-year-olds, 28​% say they have called a talk show while under the influence of peer pressure.

i.e. X no of people who say they have called a talk show while under the influence of peer pressure is binomial with p = 0.28

Each person is independent of the other and there are only two outcomes

n =7

a) the probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure

=
`P(Y\geq 1)` where Y is binomial with p = 0.72

=
`1-(1-0.72)^7\\=0.9999`

b) the probability that at least one has called a talk showcalled a talk show while under the influence of peer pressurepeer pressurethe probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure

=
`P(x\geq 1) =1-P(0)\\= 1-(1-0.28)^7\\=0.8997`