Question

a pharmaceutical company collects data on the side effects participants report for a drug it is testing. the company finds that the probability of experiencing a headache is 5 percent and the probability of experiencing both a headache and heartburn is 2 percent. if the probability of experiencing a headache or heartburn is 8 percent, what is the probability of experiencing heartburn?
1 percent
5 percent
11 percent
15 percent

Explanation:

Step1: Recall the formula for the probability of the union of two events

Let $A$ be the event of experiencing a headache and $B$ be the event of experiencing heart - burn. The formula for $P(A\cup B)$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

Step2: Identify the given probabilities

We are given that $P(A) = 0.05$, $P(A\cap B)=0.02$ and $P(A\cup B)=0.08$.

Step3: Rearrange the formula to solve for $P(B)$

From $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, we can solve for $P(B)$ as $P(B)=P(A\cup B)+P(A\cap B)-P(A)$.

Step4: Substitute the values into the formula

$P(B)=0.08 + 0.02-0.05$.
$P(B)=0.05$.

Answer:

5 percent