Question

The probability of a random adult in one country being selected with a certain virus is 0.003. In the tests for the virus, blood samples from 27 people are collected. What is the probability that the combined sample tests positive? 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

n = sample size = 27

p = probability of success = 0.003

Consider

X as random variable that is defined as blood sample of people.

We are asked to find

At least one person means

We are asked to find

We use complement rule of probability

We can find P (X = 0 ) using formula

0 ! is always 1

( Because every number has raise to 0 is always 1)

We plug values of P (X=0)

Definition for Unlikely

Otherwise it is not unlikely

Here

0.077918573 > 0.05 So it is not unlikely

Answer :-

It is nor unlikely for such combined sample to test positive , because the probability that the combined sample will test positive is greater than 0.05

I hope this will help you :)