Question

According to a study published by a group of University of Massachusetts sociologists, about 67% of the 20 million persons in this country who take Valium are women. Assume this figure to be a valid estimate. Find the probability that on a given day the eighth prescription written by a doctor for Valium is the fourth prescribing Valium for a woman.

Answer 1

To find the probability that on a given day the eighth prescription written by a doctor for Valium is the fourth prescribing Valium for a woman, we need to multiply the probability of a woman being prescribed Valium on the fourth prescription by the probability of a man being prescribed Valium on the first three prescriptions and a woman being prescribed Valium on the next four prescriptions.

Step-by-step explanation:

To find the probability that on a given day the eighth prescription written by a doctor for Valium is the fourth prescribing Valium for a woman, we need to determine the probability of a woman being prescribed Valium on the fourth prescription and then multiply it by the probability of a man being prescribed Valium on the first three prescriptions and a woman being prescribed Valium on the next four prescriptions.

According to the study, 67% of the persons who take Valium are women. Therefore, the probability of a person being a woman and being prescribed Valium is 0.67.

Now, let's calculate the probability:

1. The probability of a woman being prescribed Valium on the fourth prescription is 0.67.
2. The probability of a man being prescribed Valium on the first three prescriptions is 0.33 multiplied by itself three times (0.33^3).
3. The probability of a woman being prescribed Valium on the next four prescriptions is 0.67 raised to the power of four (0.67^4).
4. Multiply these probabilities together to find the probability that on a given day the eighth prescription written by a doctor for Valium is the fourth prescribing Valium for a woman.