SOLUTION: 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 probabi

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Question 1178009: 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 by CPhill(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break down this problem using probability notation.
**Define Events**
* **E:** Event that a subject has been exposed to the allergen.
* **R:** Event that a subject experiences an allergic reaction.
**Given Information**
* P(E ∩ R) = 0.60 (Probability of being exposed AND having a reaction)
* P(R | E) = 0.80 (Probability of having a reaction GIVEN exposure)
**Goal**
* Find P(E) (Probability of being exposed to the allergen)
**Apply Conditional Probability Formula**
We know that:
* P(R | E) = P(E ∩ R) / P(E)
We can rearrange this formula to solve for P(E):
* P(E) = P(E ∩ R) / P(R | E)
**Substitute the Given Values**
* P(E) = 0.60 / 0.80
* P(E) = 6/8
* P(E) = 3/4
* P(E) = 0.75
**Therefore, the probability that a randomly selected subject will have been exposed to the allergen is 0.75.**