Final answer:
The given statement "The variable q represents 1 - p in the success-failure condition." is true, thus the correct option is A.
Explanation:
In order to understand why the variable q represents 1 - p in the success-failure condition, we must first understand what these variables represent. In statistics, p is commonly used to represent the probability of success in a given event. Therefore, 1 - p would represent the probability of failure. Now, in a success-failure condition, there are only two possible outcomes - success or failure. This means that if the probability of success is p, then the probability of failure must be 1 - p.
But why is this represented by the variable q? This is where the concept of complementary events comes in. Complementary events are two events that cannot occur simultaneously and together, they make up the entire sample space. In this case, the events are success and failure. Since they cannot occur at the same time, the probabilities of these events must add up to 1 (or 100%). Therefore, q is used to represent the probability of failure because it is the complement of p.
To further understand this concept, let's look at an example. Let's say a company is conducting a survey to determine the percentage of customers who are satisfied with their product. The probability of a customer being satisfied is p = 0.8. This means that the probability of a customer being dissatisfied is 1 - 0.8 = 0.2, which is represented by the variable q. So, if we were to calculate the proportion of dissatisfied customers, we would use the formula q = (1 - p) = (1 - 0.8) = 0.2.
In the context of a success-failure condition, this concept can also be represented using a binomial distribution. In a binomial distribution, we have two possible outcomes - success (represented by p) and failure (represented by q). The formula for calculating the probability of x successes in n trials is P(X = x) = nCx * p^x * (1 - p)^(n-x). Here, p and (1 - p) represent the probabilities of success and failure respectively.
To conclude, the variable q represents 1 - p in the success-failure condition because it is the complement of p and together, they make up the entire sample space. It is important to understand this concept in order to accurately interpret and solve problems involving probabilities and binomial distributions, thus the correct option is A.