Question

A state lottery randomly chooses balls numbered from through without replacement. You choose numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If​ so, identify a​ success, specify the values​ n, p, and q and list the possible values of the random variable x. Is the experiment​ binomial? A. ​Yes, there are a fixed number of trials and the trials are independent of each other. B. ​No, because the probability of success is different for each trial. C. ​No, there are more than two outcomes for each trial. D. ​Yes, the probability of success is the same for each trial.

Answer 1

B. ​No, because the probability of success is different for each trial.

The experiment is not binomial.

Explanation:

The trials are not independent because they are chosen without replacement.

There are successes and failures but the trials are dependent.

So it is not binomial.

When the balls are not replaced the probability of success becomes different for each ball.

Suppose we have 10 balls and we pick out 1 so the p1 = 1/10

but when we again pick out another without replacement the p2= 1/9

This explains why it is not binomial. In binomial the n is fixed.