Based on a survey, assume that 53 percent of consumers are comfortable having dr

Question

Based on a survey, assume that 53 percent of consumers are comfortable having drones deliver their 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:

(0.53)( 0.53)(0.47)(0.47)=0.0621 ?

Choose the correct answer below.

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

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 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.

Explanation / Answer

Correct calculations:

Here first we need to find the number of ways of choosing two persons comfortable with drone. So number of ways of selecting 2 persons out of 4 is C(4,2) = 6.

So the probability that when four consumers are randomly selected, exactly two of them are comfortable with the drones is

P(exactly two of them are comfortable with the drones) = 6 * (0.53)( 0.53)(0.47)(0.47)

Answer:

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.

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