Question

About 9​% 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:

Probability of both people being allergic: 0.81%.

Probability of at least one being allergic: 17.19%

Step-by-step explanation:

If the probability of one person being allergic to pollen is 9%, the probability of two people selected being both allergic is:

0.09 * 0.09 = 0.0081 = 0.81%

The probability of at least one being allergic can be calculated with 1 minus the probability of both not being allergic.

If the probability of being allergic is 9%, the probability of not being allergic is (1 - 0.09) = 0.91 = 91%.

So, the probability of both not being allergic is:

0.91 * 0.91 = 0.8281

Then, The probability of at least one being allergic is:

1 - 0.8281 = 0.1719 = 17.19%