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) = [tex]0.17\times 0.17= 0.0289[/tex]
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) = [tex]1- (0.83\times 0.83) = 1-0.6889 = 0.3111[/tex]
Hence The the probability both are allergic to pollen is 0.0289 and the probability at least one is allergic to pollen 0.3111.
