Question

The probability that any given person is allergic to a certain drug is .03. What is the probability that none of the 3 randomly selected persons is allergic to this drug? Assume that all 3 persons are independent.

Answer 1

Answer: =0.912673

Step-by-step explanation:

Given : The probability that any given person is allergic to a certain drug :

`p=0.03`

The number of persons randomly selected = 3

Using binomial distribution,

`P(x)=^nC_xp^x(1-p)^(n-x)`, where P(x) is the probability of getting success inn x trials , n is the number of trails and p is the probability of getting success inn each trial.

Then , the probability that none of the 3 randomly selected persons is allergic to this drug:-

`P(0)=^3C_0(0.03)^0(1-0.03)^(3)=(0.97)^3=0.912673`

Hence, the probability that none of the 3 randomly selected persons is allergic to this drug = 0.912673