In the negative binomial distribution, what is q defined as?

In the negative binomial distribution, what is q defined as?

• A. The probability of success
• B. 1 - p
• C. The total number of failures
• D. The average number of failures

Answer: (B)

In the context of the negative binomial distribution, the term "q" is defined as the probability of failure on each trial. Since the probability of success is denoted by "p," it follows that the probability of failure is \( q = 1 - p \). This makes option B the correct choice. The negative binomial distribution models the number of failures that occur before a specified number of successes is achieved. Therefore, understanding the relationship between p and q is crucial in applying the distribution correctly in various probability scenarios. By defining q as \( 1 - p \), it allows for a clear distinction between the two outcomes of a trial—success and failure—enabling accurate calculations and predictions based on the distribution's parameters.

In the context of the negative binomial distribution, the term "q" is defined as the probability of failure on each trial. Since the probability of success is denoted by "p," it follows that the probability of failure is ( q = 1 - p ). This makes option B the correct choice.

The negative binomial distribution models the number of failures that occur before a specified number of successes is achieved. Therefore, understanding the relationship between p and q is crucial in applying the distribution correctly in various probability scenarios. By defining q as ( 1 - p ), it allows for a clear distinction between the two outcomes of a trial—success and failure—enabling accurate calculations and predictions based on the distribution's parameters.