Question

Based on a​ survey, assume that 42​% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six 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 four consumers not​ comfortable, as in this​ calculation: (0.42 )(0.42 )(0.58 )(0.58 )(0.58 )(0.58 )equals0.0200​?

Answer 1

See explanation

Explanation:

The calculation (0.42 )(0.42 )(0.58 )(0.58 )(0.58 )(0.58 ) describes the only one case - if first two consumers are comfortable having drones deliver their purchases and the last four are not comfortable.

When six consumers are randomly​ selected, exactly two of them are comfortable with the drones means these two consumers may be first and third, first and fourth and so on.

In general, the probability that when six consumers are randomly​ selected, exactly two of them are comfortable with the drones is

`P=C^6_2(0.42)^2(0.58)^(6-2)=15(0.42)(0.42)(0.58)(0.58)(0.58)(0.58)`