Question

Drone Deliveries Based on a Pitney Bowes survey, assume that 42% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when five 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 three consumers not comfortable, as in this calculation:$\left(0.42\right)\left(0.42\right)\left(0.58\right)\left(0.58\right)\left(0.58\right)=0.0344$

Short answer

The estimate implies that the first two consumers are comfortable with drones and the last three are not, although there are other scenarios in which two consumers are comfortable with drones, and three are not. The probabilities associated with such alternate arrangements should also be included in the results.

Step-by-step solution

Given information

It is given that 42% of consumers are comfortable having drones deliver their purchases and the rest of 58% of consumers are not comfortable having drones deliver their purchases.

Error with the calculation

An expression is noted for computing the probability of selecting exactly two consumers, out of five who are comfortable with drones, followed by three consumers who are not.

The given expression is as follows:

$\left(0.42\right)\left(0.42\right)\left(0.58\right)\left(0.58\right)\left(0.58\right)$

The estimate assumes that the first two consumers are comfortable with drones and the last three consumers are not, but there are other scenarios in which two consumers are comfortable and three are not. The results should also contain the probability associated with those alternate arrangements.