Respuesta :
Answer:
What is wrong is that the combinations were not used. It has to be used because of the different ordering that the customers may be chosen. The correct answer is 0.333
Step-by-step explanation:
For each custoer, there are only two possible outcomes. Either they are confortable with drones delivering their purchases, or they are not. Customers are independent. So the binomial distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
38% of consumers are comfortable having drones deliver their purchases.
This means that [tex]p = 0.38[/tex]
Four consumers are randomly selected
This means that [tex]n = 4[/tex]
Probability that exactly two of them are comfortable with the drones
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.38)^{2}.(0.62)^{2} = 6*(0.38)*(0.38)*(0.62)*(0.62) = 0.3330[/tex]
What is wrong is that the combinations were not used. It has to be used because of the different ordering that the customers may be chosen.
