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.

Explanation:

Analyze the conditions for a binomial experiment

$$
LATEXBLOCK0
$$

Evaluate the lottery experiment

$$
LATEXBLOCK1
$$

Match with the correct option

$$ \text{Option D correctly states: "No, because the probability of success is different for each trial."} $$

Answer:

• 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)