Question

A state lottery randomly chooses 7 balls numbered from 1 through 45 without replacement. You choose 7 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, there are more than two outcomes for each trial.
C) Yes, the probability of success is the same for each trial.
D) No, because the probability of success is different for each trial.

Answer 1

The selection of 7 balls from 45 without replacement is not a binomial experiment because the probability of success changes after each draw. So the correct option is D.

Step-by-step explanation:

The state lottery question involves determining if the selection of 7 balls from a set of 45 without replacement is a binomial experiment. A binomial experiment requires a fixed number of trials with only two possible outcomes for each trial, and the trials are independent with a constant probability of success or failure (p and q don't change). The correct answer to the question is 'No, because the probability of success is different for each trial'. When drawing balls without replacement, the odds change after each draw, making the trials dependent on previous draws. Therefore, the correct option is D.

Answer 2

Answer is D - No, because the probability of success is different for each trial.

Step-by-step explanation:

As given-

A state lottery randomly chooses 7 balls numbered from 1 through 45 without replacement.

You choose 7 numbers and purchase a lottery ticket.

Determine whether this experiment is binomial.

Answer is D - No, because the probability of success is different for each trial.