Question

Among 32​- to 37​-year-olds, 34​% say they have called a talk show while under the influence of alcohol. Suppose three 32​- to 37​-year-olds are selected at random. Complete parts​ (a) through​ (d) below.

​(a) What is the probability that all three have called a talk show while under the influence of alcohol​? ​(Round to four decimal places as​ needed.)

​(b) What is the probability that at least one has not called a talk show while under the influence of alcohol​? ​(Round to four decimal places as​ needed.) ​

(c) What is the probability that none of the three have called a talk show while under the influence of alcohol​? ​(Round to four decimal places as​ needed.)

​(d) What is the probability that at least one has called talk show while under the influence of alcohol​? ​(Round to four decimal places as​ needed.)

Answer 1

Ans:

Us binomial distribution with n=3 and p=0.34

a)

P(all three called)=0.34^3=0.0393

b)

P(at least one not called)=1-P(none of them not called)

=1-P(all three called)=1-0.0393=0.9607

c)

P(none of three called)=(1-0.34)^3=0.2875

d)P(at least one called)=1-P(none called)=1-0.2875=0.7125