The probability that any given person is allergic to a certain drug is . What is the probability that none of three randomly selected persons is allergic to this drug? Assume that all three persons are independent.

Step-by-step explanation:

Hello!

You have two possible events:

The person is allergic to the drug with probability: P(A)= 0.03

The person is not allergic to the drug, with probability: P(Ac)= 1 - (A)= 1 - 0.03= 0.97

You need to calculate the probability of choosing three persons at random and none of them is allergic to the drug then you are in the following situation:

"The first person is not allergic to the drug" AND "The second person is not allergic to the drug" AND "The third person is not allergic to the drug"

The word "and" represents the union between events and it's symbolized as: ∩

So you can symbolize the situation as:

P(Ac∩Ac∩Ac)

Since the three persons are independent you can express it as:

P(Ac)*P(Ac)*P(Ac)= 0.97*0.97*0.97= 0.97³= 0.91

I hope it helps!