Answer:
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
Hope this Helps!!!
