Question

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​?

​What is  the probability that both will be nervous around strangers

Answer 1

Given that probability p= 18/100 = 0.18 (nervous around  strangers.)

so, using negative rule

we can write that

P(not nervous around  strangers) = 1 - P(nervous around  strangers)

= 1 - 0.18

= 0.82

(A) Probability that an individual is nervous around  strangers. = p = 0.18

probability that 2 people are nervous around  strangers. = p*p

= 0.18*0.18

= 0.0324

(B) Probability that at least one is nervous around  strangers. = 1- Probability that none is nervous around  strangers.

using the P(not nervous around  strangers) = 0.82

we get

= 1- (0.82*0.82)

= 1 - 0.6724

= 0.3276