How is 'q' defined in relation to the parameter 'p' in the geometric distribution?

How is 'q' defined in relation to the parameter 'p' in the geometric distribution?

• A. q = 1 - p
• B. q = p + 1
• C. q = p/2
• D. q = p^2

Answer: (A)

In the context of the geometric distribution, 'p' represents the probability of success on a given trial, while 'q' is defined as the probability of failure on that same trial. The relationship between 'p' and 'q' can be expressed mathematically as: q = 1 - p This equation indicates that the sum of the probabilities of success (p) and failure (q) must equal 1, since every trial can either result in success or failure. Therefore, if you know the probability of success, you can easily determine the probability of failure through this simple relationship. In summary, defining 'q' as 1 - p accurately captures the fundamental nature of probabilities in the geometric distribution, verifying that both probabilities combine to total 1.

In the context of the geometric distribution, 'p' represents the probability of success on a given trial, while 'q' is defined as the probability of failure on that same trial. The relationship between 'p' and 'q' can be expressed mathematically as:

q = 1 - p

This equation indicates that the sum of the probabilities of success (p) and failure (q) must equal 1, since every trial can either result in success or failure. Therefore, if you know the probability of success, you can easily determine the probability of failure through this simple relationship.

In summary, defining 'q' as 1 - p accurately captures the fundamental nature of probabilities in the geometric distribution, verifying that both probabilities combine to total 1.