Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003. In tests for the​ virus, blood samples from 11 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

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.003

N = number of trials = 11

R = desired success = at least 1

We know that sum of all the probabilities is = 1

So, P(at least 1) = 1 - P(0)

P(at least 1) = 0.032509428381929922628516915638147

As the probability is less than 0.05

It is unlikely for such a combined sample to test positive