Question

a state lottery randomly chooses 6 balls numbered from 1 through 44 without replacement. you choose 6 numbers and purchas variable represents the number of matches on your ticket to the numbers drawn in the lottery. determine whether this experimen a success, specify the values n, p, and q and list the possible values of the random variable x. 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. list the possible values of the random variable x. choose the correct answer below. a. the possible values for x are 1, 2, 3, 4, ..., 44. b. the possible values for x are 1, 2, ..., 6. c. the experiment is not binomial.

Explanation:

Step1: Check binomial experiment conditions

A binomial experiment has the following conditions:

• Fixed number of trials \(n\).
• Two possible outcomes (success and failure).
• Probability of success \(p\) is constant for each trial.
• Trials are independent.

In this lottery experiment, the probability of success (matching a number) changes on each draw since the balls are drawn without replacement. So, it does not meet the constant - probability - of - success condition for a binomial experiment.

Step2: Determine possible values of \(x\)

Since the experiment is not binomial, we can't use the binomial framework. The number of matches \(x\) can be \(0,1,2,3,4,5,6\) (but since the experiment is not binomial, and the options given in the problem:

• Option A for possible values of \(x\) (\(1,2,\cdots,44\)) is wrong because the maximum number of matches is \(6\) (the number of balls drawn).
• Option B (\(1,2,\cdots,6\)) is wrong because \(x = 0\) (no matches) is also a possibility. But since the experiment is not binomial, and we follow the options in the problem, and the fact that the non - binomial nature is already established.

Answer:

D. The experiment is not binomial.
B. The experiment is not binomial.
C. The experiment is not binomial.