Question

a state lottery randomly chooses 6 balls numbered from 1 through 43 without replacement. you choose 6 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. no, there are more than two outcomes for each trial.
b. yes, there are a fixed number of trials and the trials are independent of each other.
c. yes, the probability of success is the same for each trial.
d. no, because the probability of success is different for each trial.

identify a success. choose the correct answer below.
a. a success is matching all of the numbers in the lottery.
b. a success is matching one of the numbers in the lottery.
c. a success is the number of matches on your ticket to the numbers drawn in the lottery.
d. the experiment is not binomial.

Explanation:

Analyze independence of trials

The lottery draws 6 balls from 43 "without replacement." Because the balls are not replaced, the probability of matching a number changes with each selection (the trials are dependent). Thus, the experiment is not binomial.

Identify a success

Since the experiment is determined to be not binomial in the first part, the corresponding option for identifying a success is that the experiment is not binomial.

Answer:

Question 1

• (A) No, there are more than two outcomes for each trial.
• (B) Yes, there are a fixed number of trials and the trials are independent of each other.
• (C) Yes, the probability of success is the same for each trial.
• (D) No, because the probability of success is different for each trial. (Correct answer)

Question 2

• (A) A success is matching all of the numbers in the lottery.
• (B) A success is matching one of the numbers in the lottery.
• (C) A success is the number of matches on your ticket to the numbers drawn in the lottery.
• (D) The experiment is not binomial. (Correct answer)