In: Statistics and Probability
According to a study published by a university, approximately two thirds of the 20 million people who consume Valium in the US are women. Suppose a doctor who specializes in anxiety problems and muscle spasms always prescribes Valium for his patients. Suppose further that the chance that the doctor will prescribe a female patient is 2/3.
a) Find the probability that the fifth prescription for Valium given by a doctor is the first Valium prescription for a woman.
b) What is the probability that the doctor will see five patients until three women receive the Valium prescription?