Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the? virus, blood samples from 25 people are combined. What is the probability that the combined sample tests positive for the? virus? Is it unlikely for such a combined sample to test? positive? Note that the combined sample tests positive if at least one person has the virus.

Answer 1

This is a Binomial distribution with the parameters:

n = 25, p = 0.004

Let X denote the random variable for the number of people infected with the virus.

In oder for the combined sample to test positive, atleast one person should test positive.

So, the probability that the combined sample tests positive is: P(X >=1 )

Using the formula:

P(X >=1) = 1 - P(X=0)

Now,

P(X=0) = ⁿC₀*(p^0)*((1-p)^(n-0)) = ²⁵C₀*(0.004^0)*((1-0.004)^(25-0)) = 0.904

So,

P(X >= 1) = 1-0.904 = 0.096