Question

About 5​% 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​? ​(a) The probability that both will be allergic to pollen is nothing. ​(Round to four decimal places as​ needed.) ​(b) The probability that at least one person is allergic to pollen is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

a) 0.0025

b) 0.0975

Explanation:

We are given the following in the question:

About 5​% of the population of a large country is allergic to pollen.

Thus, probability that an individual has allergy is 0.05

P(allergic) = 0.05

P(Not allergic) = 1 - 0.05 = 0.95

If A and B are independent even, then,

`P(A\cap B) = P(A) * P(B)`

Two people are randomly selected.

a) P( both will be allergic to pollen)

Since these are independent event,

`\text{P(both will be allergic to pollen)} = \text{P(Allergic)}* \text{P(Allergicr)}\\= 0.05* 0.05 = 0.0025`

b) P(at least one person is allergic to pollen)

`= 1 - \text{P(both not allergic to pollen)}\\= 1 -( \text{P(Not allergic)}* \text{P(Not allergic)})\\=1 - (0.95* 0.95)\\= 0.0975`