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 .60. The probability is .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 or she will have been exposed to the allergen?

Answer 1

Answer: Our required probability would be 0.75.

Explanation:

Since we have given that

Probability that subject will have been exposed to a certain allergen and experience a reaction to the allergen = 0.60

Probability that subject exposed to the allergen will experience an allergic reaction = 0.80

Let Probability that he will have been exposed to the allergen be 'x'.

By multiplication law of probability, we get that

`0.8x=0.6\\\\x=(0.6)/(0.8)\\\\x=0.75`

Hence, our required probability would be 0.75.