a pharmaceutical company collects data on the side effects participants report for a drug it is testing. the…

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?\n1 percent\n5 percent\n11 percent\n15 percent

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?\n1 percent\n5 percent\n11 percent\n15 percent

Answer

Explanation:

Step1: Define the probability formula

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

Step2: Substitute the known values

We know that $P(A) = 0.05$, $P(A\cap B)=0.02$, and $P(A\cup B)=0.08$. Substituting into the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, we get $0.08 = 0.05+P(B)-0.02$.

Step3: Solve for $P(B)$

First, simplify the right - hand side of the equation: $0.05 + P(B)-0.02=0.03 + P(B)$. Then, solve the equation $0.08=0.03 + P(B)$ for $P(B)$ by subtracting 0.03 from both sides. So, $P(B)=0.08 - 0.03=0.05$.

Answer:

5 percent