A random sample of 100 people from a town were administered

A random sample of 100 people from a town were administered a diagnostic test for presence of a virus, of whom 55 tested positive. It is known that the probability that a person in the general population of the town carries the virus is very close to 0.50. We also know that the probability that a person carries the virus given that she/he has tested positive is 0.8. -i- Find the probability that a person tests positive and actually carries the virus. -ii- Find the probability that a person tests negative and does not actually carry the virus.

Solution

i)

P(positive and carries) = P(positive) P(carries|positive) = (55/100)(0.8) = 0.44 [answer]

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ii)

Consider the table:

Thus, P(negative and not carry) = 39/100 = 0.39 [answer]

	Test Positive	Test Negative
Carries Virus	44	6	50
Does not carry virus	11	39	50
Totals	55	45	100