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 probability formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of having a headache, $B$ is the event of having heart - burn, $P(A\cup B)$ is the probability of having a headache or heart - burn, $P(A)$ is the probability of having a headache, $P(B)$ is the probability of having heart - burn, and $P(A\cap B)$ is the probability of having both.
Let $P(A) = 0.05$, $P(A\cap B)=0.02$, and $P(A\cup B)=0.08$.

Step2: Rearrange the formula to solve for $P(B)$

$P(B)=P(A\cup B)+P(A\cap B)-P(A)$.
Substitute the given values: $P(B)=0.08 + 0.02-0.05$.

Step3: Calculate the result

$P(B)=0.05$.

Answer:

5 percent