Question

Lawrence likes to shoot a bow and arrow in his free time. On any shot, he has about a 10% chance of hitting the bull's-eye. As a

challenge one day, Lawrence decides to keep shooting until he gets a bull's-eye. Let Y = the number of shots he takes.
Does this scenario describe a binomial setting? Justify your answer.

A) Yes, this is a binomial setting and X has a binomial distribution with n = 10 and p = 0.10.

B) No, this is not a binomial setting because the probability of success is not the same for each trial.

C) No, this is not a binomial setting because the given scenario is not binary.

D) No, this is not a binomial setting because there are not a fixed number of trials.

E) No, this is not a binomial setting because the trials are not independent.

Answer 1

The scenario with Lawrence does not represent a binomial setting; it represents a geometric setting since the number of trials is not fixed and we're looking for the number of trials until the first success.

Step-by-step explanation:

The scenario with Lawrence shooting arrows until he hits a bull's-eye does not describe a binomial setting because the number of trials is not fixed in advance. In a binomial distribution, there are a fixed number of trials (n), only two possible outcomes (success or failure), and the trials must be independent and conducted under identical conditions. Lawrence's scenario is actually an example of a geometric setting, where the exact number of trials is not known beforehand and we are interested in the number of trials it takes until the first success occurs.

Therefore, the correct answer to the question is:

D) No, this is not a binomial setting because there are not a fixed number of trials.

Answer 2

Lawrence's archery practice is not a binomial setting because it lacks a fixed number of trials, which is one of the key requirements for a binomial distribution.

Step-by-step explanation:

The scenario where Lawrence decides to keep shooting until he gets a bull's-eye does not describe a binomial setting. For a scenario to be described as a binomial setting, it must have a fixed number of trials, two possible outcomes (success or failure), and the trials must be independent with the probability of success being the same on each trial. Lawrence shooting until he hits the bull's-eye does not have a fixed number of trials; rather, he will continue until he achieves a success, which could take any number of trials. Therefore, the correct answer here is:

D) No, this is not a binomial setting because there are not a fixed number of trials.

This description differs from a geometric problem, where you may have any number of failures before the desired success, with the probability of success remaining constant for each trial.