Question

a. According to a study published by a group of University of Massachusetts sociologists,  about C of the 20 million persons in this country who take Valium are women. Assuming this figure to be a valid estimate.Calculate the probability that on a given day the fifth prescription written by a doctor for Valium is the first prescribing Valium for a woman.  

Answer 1

Consider that prescribing valium for a person is a trial.

We consider it a success if a prescription of valium is for a woman.

Probability of a success in eacn trial is $p = \frac{2}{3}$

Therefore, probability of a failure in each trial is $q = 1 – p = \frac{1}{3}$

the probability that on a given day the fifth prescription written by a doctor for Valium is the first prescribing Valium for a woman is

$pq^{x-1} = \frac{2}{3}(\frac{1}{3})^{5-1} \\ = \frac{2}{3} \times \frac{1}{18} \\ = \frac{2}{243} \\ = 0.008$