Question

The probability of a randomly selected adult in one country being infected with a certains virus is 0.004. In tests for the virus, blood samples from 18 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.
The probability that the combined sample will test positive is ___
I have seen others ask these kind of questions, but their examples are not working from my side, can anyone give step by step instructions as to how to solve this?

Answer 1

The probability that the combined sample will test positive is 0,0696.

Explanation:

The combined sample tests positive if at least one person has the virus. To calculate this probability, we need to calculate the probability that all in the combined sample test is negative and subtract from 1.

P(At least one adult in the combined sample tests has virus) =

1 - P( All adults in the combined sample tests do not have virus)

Since the probability of a randomly selected adult in one country being infected with a certain virus is 0.004,

the probability of a randomly selected adult in one country being not infected with a certain virus is 1-0.004=0.996

And the probability that all adults in the combined sample tests do not have virus =

`0.996^(18)`

Therefore the probability that at least one adult in the combined sample tests has virus is 1-
`0.996^(18)` ≈ 0,0696