Question

A state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement. You choose 4 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

A) Yes, there are a fixed number of trials and the trials are independent of each other.

Sample size 'n' = 37

probability of success p = 0.1081

q = 0.8919

Explanation:

Explanation:-

Given data we will observe that

There are a fixed number of trials and the trials are independent of each other.

Given a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.

Given size 'n' = 37

The probability that a state lottery randomly chooses 4 balls numbered from 1 through 37 without replacement.

Proportion

`p = (x)/(n) = (4)/(37) = 0.1081`

q = 1 - p = 1 - 0.1081 = 0.8919

Final answer:-

Sample size 'n' = 37

p = 0.1081

q = 0.8919