Question

A few people who have a particular disease take part in a medical trial that tests the effect of a medicine on the disease. Half the people are given medicine and the other half are given sugar pills, which have no effect on the disease. The medicine has a 60% chance of curing someone, but people who do not get the medicine still have a 10% chance of getting well. The probability that a person gets well is %, and the probability that the person was cured because of the medicine is %.

Answer 1

The probability that a person gets well can be calculated by multiplying the probability of being cured by the medicine by the probability of not getting the medicine. The probability that a person was cured because of the medicine can be calculated by dividing the probability of being cured by the medicine by the probability of getting well.

Step-by-step explanation:

The probability that a person gets well can be calculated by multiplying the probability of being cured by the medicine by the probability of not getting the medicine:

Probability of getting well = Probability of being cured x Probability of getting the medicine + Probability of not being cured x Probability of not getting the medicine

Given that the medicine has a 60% chance of curing someone and people who do not get the medicine still have a 10% chance of getting well:

Probability of getting well = 0.6 x 0.5 + 0.1 x 0.5 = 0.3 + 0.05 = 0.35 = 35%

The probability that a person was cured because of the medicine can be calculated by dividing the probability of being cured by the medicine by the probability of getting well:

Probability that the person was cured because of the medicine = Probability of being cured x Probability of getting the medicine / Probability of getting well

Given that the medicine has a 60% chance of curing someone:

Probability that the person was cured because of the medicine = 0.6 x 0.5 / 0.35 = 0.3 / 0.35 = 0.857 = 85.7%