Question

About 55​% of the population of a large country is allergic to pollenallergic to pollen. If two people are randomly​ selected, what is the probability both are allergic to pollenallergic to pollen​? What is the probability at least one is allergic to pollenallergic to pollen​?

Answer 1

Both = 0.3025 or 30.25%

At least one = 0.7975 or 79.75%

Explanation:

The probability that one of the two is allergic to pollen is 55% so the probability that both are allergic is given by:

`P_(both) = 0.55^(2) = 0.3025\\`

The probability of at least one of them being allergic can be given by the whole minus the probability of neither being allergic:

`P_(1) = 1 - (1- 0.55)^(2) = 0.7975\\`