Question

# The probability of a randomly selected adult in one country being infected with a certain virus...

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.

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

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