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

Answer 1

Let H = headache, B = heartburn. By inclusion–exclusion:

P(H ∪ B) = P(H) + P(B) − P(H ∩ B).

So P(B) = P(H ∪ B) − P(H) + P(H ∩ B) = 0.08 − 0.05 + 0.02 = 0.05 = 5%.

Answer: 5 percent.