Question

In a completely ethical experiment, an experimental drug that gives super powers is given to 70% of its subjects while other subjects recieved a placebo. The results show that 58% of those given the drug developed super powers but in the group given the placebo only 10% gained super powers. Answer the following questions based off of this information.

(a) You hear about one of the subjects of this experiment using telekinsis to lift objects later that day. What is the probability that this subject recieved the experimental drug?

(b) What is the probability that a subject is given the placebo and they do not get super powers?

(c) What is the probability that a subject gained super powers?

Answer 1

a) P(received an experimental drug) = 0.7

b) P(get super power | given placebo) = 0.10

or, P( get super power and given placebo)/P(given placebo) = 0.1

or, P(get super power and given placebo) = 0.1 * P(given placebo)

or, P(get super power and given placebo) = 0.1 * 0.3 = 0.03

P(given placebo and nor get super powers) = P(given placebo) - P(given placebo and get super powers)

                                                                      = 0.3 - 0.03 = 0.27

c) P(gained super powers) = 0.7 * 0.58 + 0.3 * 0.1 = 0.436