Question

A survey on healthy choices was given to gym members at Work It Out. The results showed that 90% of its members drank protein shakes. Of the members who drank protein shakes, 30% took weight-loss medication whereas only 10% of members who did NOT drink protein shakes took weight-loss medication. What is the probability that a gym member does NOT take weight-loss medication?

Answer 1

Probability that a gym member does not take weight-loss medication = 0.63

Explanation:

Let E be the event of choosing a gym member who drank protein shakes and W be the event of choosing a gym member who took weight loss medication.

Probability that a gym member drank protein shakes = P(E) = 0.9

Probability that a gym member does not drink protein shakes = P(not E) = 0.1

E and W are independent events.

By using Bayes Theorem, P(E and W) = P(E)*P(W)

Probability that a gym member drank protein shakes and took weight loss medication = P(E and W) = 0.3*0.9 = 0.27

Probability that a gym member took weight-loss medication = P(W) = 0.1 + 0.27 = 0.37

(10% of members who did not drink protein shakes took weight-loss medication)

Therefore, Probability that a gym member does not take weight loss medication = P(not W) = 1 - 0.37 = 0.63