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: (0.42) (0.42) (0.58) (0.58) (0.58) = 0.0344?

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Step 1   The given scenario is relative to a binomial probability distribution.   Binomial probability distribution:  f(x)=(beg∈{array}{c}n∖xend{array})px(1−p)n−x  Where,  n represents the total number of trials or the sample size.  x represents the number of successes in a single trial.  p represents the probability of success in a single trial.  1−p represents the probability of failure.  Step 2   Here,   There are five consumers who were randomly selected, out of which exactly two of the consumers are comfortable with drones. Thus, the possible arrangements of getting two consumers who are comfortable the drones is,  5C2=5!2!(5−2)!  =10 ways  Step 3   Thus, there are 10 ways to get two consumers who are comfortable with the drones and the remaining three who are not comfortable with the drones.   The given answer calculated using multiplication rule represents the probability corresponding to one of the 10 possible arrangements. Similarly, the probabilities corresponding to the remaining 9 possible arrangements have to be included.   Thus, the required probability would be, 0.0344×10=0.344. Since, there are 10 possible arrangements.

Drone Deliveries Based on a Pitney Bowes survey, assume that 42% of consumers ar

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