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
Ask by Burton Carter. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability of experiencing heartburn is 5 percent.
Solution
To find the probability of experiencing heartburn (\( P(B) \)), we can use the principle of inclusion-exclusion for probabilities:
\[
P(H \text{ or } B) = P(H) + P(B) - P(H \text{ and } B)
\]
Given:
- \( P(H) = 5\% \) (probability of experiencing a headache)
- \( P(H \text{ and } B) = 2\% \) (probability of experiencing both a headache and heartburn)
- \( P(H \text{ or } B) = 8\% \) (probability of experiencing either a headache or heartburn)
Plugging in the values:
\[
8\% = 5\% + P(B) - 2\%
\]
\[
8\% = 3\% + P(B)
\]
\[
P(B) = 8\% - 3\% = 5\%
\]
**Answer:** 5 percent
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Simplify this solution Bonus Knowledge
To find the probability of experiencing heartburn, we can use the formula for the probability of the union of two events: P(Headache or Heartburn) = P(Headache) + P(Heartburn) - P(Headache and Heartburn). We know that: - P(Headache) = 0.05 (5 percent), - P(Headache and Heartburn) = 0.02 (2 percent), - P(Headache or Heartburn) = 0.08 (8 percent). Plugging in the values, we have: 0.08 = 0.05 + P(Heartburn) - 0.02. Rearranging gives us: P(Heartburn) = 0.08 - 0.05 + 0.02 = 0.05 (or 5 percent). So, the probability of experiencing heartburn is 5 percent.
