Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. A football player who completes 41% of his passes is asked to throw passes until he misses. The number of passes attempted is recorded. Does the probability experiment represent a binomial experiment? A. No, because the experiment is not performed a fixed number of times. B. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. C. Yes, because the experiment satisfies all the criteria for a binomial experiment. D. No, because there are more than two mutually exclusive outcomes for each trial.
Accepted Solution
A:
Answer:A. No, because the experiment is not performed a fixed number of times.Step-by-step explanation:Binomial probability distributionThe binomial probability is the probability of exactly x successes on n repeated trials(n is fixed), and X can only have two outcomes.[tex]P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}[/tex]In which [tex]C_{n,x}[/tex] is the number of different combinatios 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 [tex]\pi[/tex] is the probability of X happening.In this problem, we dont have a fixed number of trials. So the correct answer is:A. No, because the experiment is not performed a fixed number of times.