Final answer:
To find the probability that on a given day the fifth prescription written by a doctor for Valium is the third prescribing Valium for a woman, we need to use the information from the study that states about two-thirds of the 20 million individuals who take Valium are women. The probability can be calculated using the concept of conditional probability, by dividing the number of ways to get the desired outcome by the total number of outcomes. In this case, the probability is 1/100, or 0.01, or 1%.
Step-by-step explanation:
To find the probability that on a given day the fifth prescription written by a doctor for Valium is the third prescribing Valium for a woman, we need to use the information from the study that states about two-thirds of the 20 million individuals who take Valium are women.
Let's break down the problem. Suppose we have 100 prescriptions written for Valium by a doctor on a given day. Since two-thirds of the individuals taking Valium are women, we can calculate the probability of a prescription being written for a woman as follows:
- Calculate the number of prescriptions for women: 100 prescriptions x 2/3 = 67 prescriptions for women
- Calculate the probability that the fifth prescription written by a doctor for Valium is the third prescribing Valium for a woman:
The probability is calculated by using the concept of conditional probability. It is calculated as the probability that the fifth prescription is the third prescribing Valium for a woman among the 67 prescriptions for women. Since we have already determined the number of prescriptions for women, we can use this information to calculate the probability.
The probability of the fifth prescription being the third prescribing Valium for a woman is:
Probability = (Number of ways to get the desired outcome) / (Total number of outcomes)
The desired outcome is that the fifth prescription is the third prescribing Valium for a woman. So, the number of ways to get this outcome is 1 (since there is only one way for this to happen).
The total number of outcomes is the total number of prescriptions written for Valium, which is 100.
Therefore, the probability is 1/100, which can also be simplified to 0.01 or 1%.