Question

the effect on an antidepressant drug varies from person to person.suppose that the drug is effective on 80% of women and 65% of man.it is known that 66% of the women who take the drug are women.

i) what is the probability that the drug is effective?
ii) suppose that you are told that the drug is effective.what is the probability that the drug taker is a man..?

Answer 1

Answer on Question #43572 – Math - Statistics and Probability

The effect on an antidepressant drug varies from person to person. Suppose that the drug is effective on 80% of women and 65% of man. It is known that 66% of the people who take the drug are women.

i) What is the probability that the drug is effective?

ii) Suppose that you are told that the drug is effective. What is the probability that the drug taker is a man...?

Solution

i) The probability that the drug is effective

$$P(\text{effective}) = \frac{N_{\text{man}}}{N} \cdot P(\text{manefective}) + \frac{N_{\text{women}}}{N} \cdot P(\text{womeneffective}).$$ $$P(\text{effective}) = 0.34 \cdot 0.65 + 0.66 \cdot 0.8 = 0.749.$$

ii) The probability that the drug taker is a man

$$P(\text{drug taker is a man}) = P(\text{effective}) \cdot \frac{N_{\text{man}}}{N} = 0.749 \cdot 0.34 = 0.25466.$$

Answer: i) 0.749; ii) 0.25466.

www.AssignmentExpert.com