Question

The effects of an antidepressant drug varies from person to person. Suppose that the drug is effective on 89% of women and 65% of men. It is known that 66% of the people who take the drug are women. What is the probability?

Answer 1

Answer:

The probability that the drug is effective is 0.8084

Step-by-step explanation:

Let the following events be:

E: the drug is effective

W: the person is a woman

M: the person is a man

We know that the drug is effective on 89% of women and 65% of men, so it can be expressed as:

P(E|W): Probability that the drug is effective since the person is a woman

P(E|W)= 0.89

P(E|M): Probability that the drug is effective since the person is a man

P(E|M)= 0.65

We also know that 66% of the people who take the drug are women.

P(W)= 0.66

Then

P(M)= 1 - P(W)= 1 - 0.66 = 0.34

With all this information we can build the probability tree (attached picture) and apply the Hayes theorem:

P(E) = P(W) × P(E|W) + P(M) × P(E|M)

P(E) = 0.66 × 0.89 + 0.34 × 0.65= 0.8084