Question

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.

Answer 1

A. ​No, because the experiment is not performed a fixed number of times.

Explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials(n is fixed), and X can only have two outcomes.

`P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)`

In which
`C_(n,x)` is the number of different combinatios of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And
`\pi` 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.