Question

A drug manufacturer believes that there is a 95% chance that the drug controller will approve a new drug. The current testing shows no side effects. The manufacturer believes there is a 0.50 probability that the drug will be approved even if side effects occur. The drug manufacturer believes there is a 0.20 probability that tests will show side effects. If the drug is approved, the probability that it causes side effects is \(\underline{\hspace{2cm}}\). (rounded off to three decimal places)

Hint:

Bayes' Theorem helps to calculate conditional probability given prior probabilities.

Answer 1

Correct Answer: 0.111

Bayes' Theorem formula: \[ P(\text{Side Effects} \mid \text{Approved}) = \frac{P(\text{Approved} \mid \text{Side Effects}) P(\text{Side Effects})}{P(\text{Approved})} \] Given: \[ P(\text{Approved}) = 0.95, P(\text{Side Effects}) = 0.20, P(\text{Approved} \mid \text{Side Effects}) = 0.50 \] Thus: \[ P(\text{Side Effects} \mid \text{Approved}) = \frac{0.50 \times 0.20}{0.95} = \frac{0.10}{0.95} = 0.105 \] \[ \boxed{0.105} \]