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?

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) =

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) =

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