Based on a​ survey, assume that

26​%

of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when

five

consumers are randomly​ selected, exactly two of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

In this problem, we are working with a binomial distribution, which describes the probability of having a certain number of successes in a fixed number of trials. Here, the "success" is that a consumer is comfortable with delivery by drones. 

The values for \( n \), \( x \), \( p \), and \( q \) are as follows:

- \( n \): This is the number of trials (the number of consumers surveyed). Since five consumers are randomly selected, \( n = 5 \).
- \( x \): This is the number of successes (the number of consumers who are comfortable with drone delivery). In this case, we are asked to find the probability that exactly two of the consumers are comfortable with drone delivery, so \( x = 2 \).
- \( p \): This is the probability of success on a single trial (the probability that a consumer is comfortable with drone delivery). From the survey, we know that 26% of consumers are comfortable with drone delivery, so \( p = 0.26 \).
- \( q \): This is the probability of failure on a single trial (the probability that a consumer is not comfortable with drone delivery). Since \( q = 1 - p \), we have \( q = 1 - 0.26 = 0.74 \).

To summarize:

- \( n = 5 \)
- \( x = 2 \)
- \( p = 0.26 \)
- \( q = 0.74 \)

Would you like a step-by-step solution to calculate the probability using these values?

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**Related questions:**
1. How do you calculate the probability for a binomial distribution?
2. What is the binomial probability formula?
3. What are the key differences between binomial and normal distributions?
4. How do changes in \( p \) affect the probability of success in binomial trials?
5. How would the problem change if more consumers were surveyed?

**Tip:** In a binomial distribution, \( q \) is always the complement of \( p \) and ensures that the total probability equals 1.

Based on a​ survey, assume that 26% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

Find the probability that exactly 2 out of 5 consumers are comfortable with drone deliveries, based on a survey where 26% of consumers are in favor. This problem covers binomial distribution concepts, key formulas, and step-by-step calculations. Ideal for students in Grades 10-12 studying probability.

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