Question

About 17​% of the population of a large country is allergic to pollen. If two people are randomly​ selected, what is the probability both are allergic to pollen​? What is the probability at least one is allergic to pollen​?

Answer 1

Answer:

The the probability both are allergic to pollen is 0.0289 and the probability at least one is allergic to pollen 0.3111.

Step-by-step explanation:

Given:

About 17​% of the population of a large country is allergic to pollen.

So we can say that;

The Probability of individual to be allergic is 0.17

P(allergic) = 0.17

P(non-allergic) = 1 - 0.17 = 0.83

If 2 people are randomly selected be and individual events.

So we can say that;

P(A∩B) = P(A) × P(B)

Now we will find the Probability that both are allergic.

1) P(Both Allergic) = P(allergic) × P(allergic) = $0.17\times 0.17= 0.0289$

2) P(at least one Allergic) = 1 - P(both non-allergic)

P(at least one Allergic) = 1 - (P(non-allergic) ×  P(non-allergic))

P(at least one Allergic) = $1- (0.83\times 0.83) = 1-0.6889 = 0.3111$

Hence The the probability both are allergic to pollen is 0.0289 and the probability at least one is allergic to pollen 0.3111.