# EBook Problems Prob Basics

## Contents

## EBook Problems Set - Fundamentals

### Problem 1

In a large midwestern university with 30 different departments, the university is considering eliminating standardized scores from their admission requirements. The university wants to find out whether the students agree with this plan. They decide to randomly select 100 students from each department, send them a survey, and follow up with a phone call if they do not return the survey within a week. What kind of sampling plan did they use?

- Choose one answer.

*(a) Stratified random sampling*

*(b) Simple random sampling*

*(c) Multi-stage sampling*

*(d) Cluster sampling*

### Problem 2

It is believed that 5% of elementary school children have some kind of ADD (Attention Deficit Disorder). Researchers are hoping to track 60 or more of these students for several years. They decide to test 1500 first graders for this problem. What is the probability that they will find enough subjects for their study?

- Choose one answer.

*(a) Cannot be calculated with the given data*

*(b) More than 95%*

*(c) Less than 5%*

*(d) Between 70% to 80%*

### Problem 3

A box contains 6 balls, where 2 are red, 2 are white, and 2 are blue. Four balls are picked at random, one at a time. Each time a ball is picked, the color is recorded, and the ball is put back in the box. If the first 3 balls are red, what color is the fourth ball most likely to be?

- Choose one answer.

*(a) Red*

*(b) White*

*(c) Blue*

*(d) Blue and white are equally likely and more likely than red.*

*(e) Red, blue, and white are all equally likely.*

### Problem 4

A coin is tossed 400 times and 170 heads are observed. This coin is

- Choose one answer.

*(a) fair, because the probability of seeing that amount of heads or less is approximately 0.0013*

*(b) neither fair or unfair. There is not enough information to determine that.*

*(c) fair, because the probability of seeing that amount of heads or less is approximately 0.5*

*(d) not fair, because the probability of seeing that amount of heads or less is close to 0.*

### Problem 5

According to government data, 30% of single parents own a home. A study of the housing situation of single parents is based on a random sample of 400 single parents. What is the probability that the proportion of single parents owning a home in the sample is larger than 35%?

- Choose one answer.

*(a) 1.3*

*(b) 0.156*

*(c) 0.23*

*(d) None of the above*

### Problem 6

A fair coin is tossed, and it lands heads up. The coin is to be tossed a second time. What is the probability that the second toss will also be a head?

- Choose one answer.

*(a) 1/3*

*(b) 1/4*

*(c) Slightly less than 1/2*

*(d) Slightly more than 1/2*

*(e) 1/2*

### Problem 7

If a fair die is rolled eight times, which of the following ordered sequences of results, if any, is least likely to occur?

- Choose one answer.

*(a) 2 1 4 3 1 5 4 6*

*(b) 6 4 3 2 4 1 5 6*

*(c) 2 3 4 5 6 1 2 3*

*(d) All sequences are equally likely*

*(e) 5 6 2 6 3 5 4 2*

### Problem 8

When three fair dice are simultaneously thrown, which of the following results is most likely to be obtained?

- Choose one answer.

*(a) All three results are equally likely.*

*(b) A 5, a 3 and a 6 in any order*

*(c) Two 5's and a 3*

*(d) Three 5's*

### Problem 9

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour:

Repair calls | 0 | 1 | 2 | 3 |

P(x) | 0.1 | 0.3 | 0.4 | 0.2 |

The probability that the number of repair calls is at least 2 is:

- Choose one answer.

*(a) 0.8*

*(b) 0.2*

*(c) 0.4*

*(d) 0.6*