Question 1178009
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.**