Question 1186892: 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)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem using conditional probability:
Let's define the events:
* E: The subject has been exposed to the allergen.
* R: The subject experiences a reaction to the allergen.
We are given the following probabilities:
* P(E ∩ R) = 0.60 (Probability of exposure *and* reaction)
* P(R|E) = 0.80 (Probability of reaction *given* exposure)
We want to find P(E), the probability that a subject has been exposed to the allergen.
We can use the formula for conditional probability:
P(R|E) = P(E ∩ R) / P(E)
Rearranging this formula to solve for P(E), we get:
P(E) = P(E ∩ R) / P(R|E)
Now, plug in the given values:
P(E) = 0.60 / 0.80
P(E) = 0.75
Therefore, the probability that a randomly selected subject will have been exposed to the allergen is 0.75, or 75%.
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