SOLUTION: About 18​% of the population of a large country is nervous around strangers. If two people are randomly​ selected, what is the probability both are nervous around strangers​?

Algebra ->  Probability-and-statistics -> SOLUTION: About 18​% of the population of a large country is nervous around strangers. If two people are randomly​ selected, what is the probability both are nervous around strangers​?      Log On


   

Question 1202671: About 18​% of the population of a large country is nervous around strangers. If two people are randomly​ selected, what is the probability both are nervous around strangers​? What is the probability at least one is nervous around strangers​? Assume the events are independent.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
About 18​% of the population of a large country is nervous around strangers.
If two people are randomly​ selected, what is the probability
(a) what is the probability both are nervous around strangers​?
(b) What is the probability at least one is nervous around strangers​?
Assume the events are independent.
~~~~~~~~~~~~~~~~~~ 

(a)  P = 0.18*0.18 = 0.0324.    ANSWER


(b)  P = 1 - (1-0.18)*(1-0.18) = 1 - 0.82*0.82 = 0.3276.    ANSWER

     Here 1-0.18 = 0.82 is the probability that a randomly selected person is not nervous about strangers.
     and the product 0.82*0.82 is the probability that two randomly selected persons are not nervous about strangers.
     So, the complement  1 - 0.82^2  is the probability that at least one of two is nervous.

Solved.