Answer to Question #118723 in Statistics and Probability for Carmen

Question

In a certain population the probability that a randomly selected subject will have been exposed to a certain allergen and experience a reaction to the allergen is 0.6. The probability is 0.8 that a subject exposed to the allergen will experience an allergic reaction. If a subject is selected at random from this population what is the probability that he/she will have been exposed to the allergen?

Answer 1

Let A = the event that the subject will have been exposed to a certain allergen

and B = the event that the subject will experience a reaction to the allergen

Then P(A ⋂ B) = 0.6 and P(B | A) = 0.8

Therefore, the probability that the subject will have been exposed to the allergen

= P(A)

= P(A ⋂ B)/P(B | A) [since, P(A ⋂ B) = P(A).P(B | A)]

= 0.6/0.8

= 0.75

Answer: The probability that the subject will have been exposed to the allergen is 0.75.