Question

a state lottery randomly chooses 6 balls numbered from 1 through 44 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.

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 the number of matches on your ticket to the numbers drawn in the lottery.
c. a success is matching one of the numbers in the lottery.
d. the experiment is not binomial.

specify the values n, p, and q. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. n = □, p = □, q = □
(type integers or decimals.)
b. the experiment is not binomial.

Explanation:

A binomial experiment has the following properties:

• Fixed number of trials (\(n\)).
• Each trial has only two outcomes (success or failure).
• The probability of success (\(p\)) is the same for each trial.
• The trials are independent.

In the lottery experiment, the balls are chosen without replacement. So, the probability of success (matching a number) changes for each trial. For example, the probability of matching the first number is \(\frac{6}{44}\), and if the first number is matched, the probability of matching the second number is \(\frac{5}{43}\) (since one ball is already drawn).

Since the probability of success is not the same for each trial, the experiment is not binomial.

Answer:

D. No, because the probability of success is different for each trial.
D. The experiment is not binomial.
B. The experiment is not binomial.