In order to determine the effectiveness of a new measles antibody test, it is administered to 500 people chosen at random. The new test was positive when administered to 96% of those who have the antibodies and it also gave positive results in 2% of those who do not have them. Based on these results, what is the probability that a randomly chosen person has measles antibodies in his/her blood if the new test is positive?

The probability that a randomly chosen person has measles antibodies in his/her blood if the new test is positive = 0.9796

Step-by-step explanation:

The event that someone tests positive = P(T)

The event that someone has antibodies = P(A)

The event that someone does not have antibodies = P(A')

The new test was positive when administered to 96% of those who have the antibodies.

This probability = P(T n A) = 0.96

The new test gave positive results in 2% of those who do not have them.

This probability = P(T n A') = 0.02

The probability that a randomly chosen person has measles antibodies in his/her blood if the new test is positive = P(A|T)

This conditional probability is given as

P(A|T) = P(T n A) ÷ P(T)

P(T) is given as

P(T) = P(T n A) + P(T n A') = 0.96 + 0.02 = 0.98

P(A|T) = P(T n A) ÷ P(T) = 0.96 ÷ 0.98 = 0.9796

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