Respuesta :
Answer:
a) 0.0025
b) 0.0975
Step-by-step 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,
[tex]P(A\cap B) = P(A) \times P(B)[/tex]
Two people are randomly selected.
a) P( both will be allergic to pollen)
Since these are independent event,
[tex]\text{P(both will be allergic to pollen)} = \text{P(Allergic)}\times \text{P(Allergicr)}\\= 0.05\times 0.05 = 0.0025[/tex]
b) P(at least one person is allergic to pollen)
[tex]= 1 - \text{P(both not allergic to pollen)}\\= 1 -( \text{P(Not allergic)}\times \text{P(Not allergic)})\\=1 - (0.95\times 0.95)\\= 0.0975[/tex]
