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
