The probability of a randomly selected adult in one country being infected with

Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.002. In tests for the virus, blood samples from 28 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.

a) What is the probability that the combined sample will test positive?

b)Is it unlikely for such a combined sample to test positive?

Explanation / Answer

a) P(Combine test will result positive)

= P(At least 1 of 28 people have virus)

= 1 - P(None out of 28 people have virus)

= 1 - (0.998)28

= 0.0545 [Rounded off to 4 decimal places]

b) No, it is not unlikely because the probability is greater than 0.05

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