Based on a survey, assume that 42% of consumers are comfortable having drones delivetheir purchases. Suppose we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by two consumers not comfortable, as in this calculation: (0.42)(0.42)(0.58)=0.0593 A. There are other arrangements consisting of two consumers who are comfortable, and two who are not. The probabilities corresponding to those other arrangements should also be included in the result. B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones. C. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones. D. The calculation assumes that the first two consumers are comfortable with drones and the last two are not, but this arrangemnent is not possible.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Based on a survey, assume that 42% of consumers are comfortable having drones delivetheir purchases. Suppose we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by two consumers not comfortable, as in this calculation: (0.42)(0.42)(0.58)=0.0593

A. There are other arrangements consisting of two consumers who are comfortable, and two who are not. The probabilities corresponding to those other arrangements should also be included in the result.

B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones.

C. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones.

D. The calculation assumes that the first two consumers are comfortable with drones and the last two are not, but this arrangemnent is not possible.

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