Question

Based on a survey assume that 35% of consumers are comfortable having drones deliver their purchases. suppose we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of three consumers comfortable with drones followed by two consumers not comfortable.

A. There are other arrangements consisting of three 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 three 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 independent of the probability of the first consumer being comfortable with drones.

Answer 1

Answer :

If we apply the mulitpliction rule, we need to multiply the 0.35 by 3 times and 0.65 by two times.

So as per the mulitplicaiton rule, we have probability of = 0.35* 0.35 * 0.35 *0.65 *0.65

As this is the hypergeometric distiribtuion.

But, we can say that order of personn might be differen who choose the delivery by the drone and who doesn't want.

for e.g. in the given table all the possible combination:

Instance/Person	1	2	3	4	5
1	0.35	0.35	0.35	0.65	0.65
2	0.35	0.35	0.65	0.35	0.65
3	0.35	0.35	0.65	0.65	0.35
4	0.35	0.65	0.35	0.35	0.65
5	0.35	0.65	0.65	0.35	0.35
6	0.35	0.65	0.35	0.65	0.35
7	0.35	0.65	0.65	0.35	0.35
8	0.65	0.35	0.35	0.35	0.65
9	0.65	0.35	0.35	0.65	0.35
10	0.65	0.65	0.35	0.35	0.35

These are the possibilities, where 0.35 inidictes that there are favour to drone delivery.

So by mulitplication rule, we are taking only one instance. While we have 10 such instances so we need to mulitply by the 10 to the mulitplication rule.

So correct answer is option A:

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