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

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