# EBook Problems Prob Basics

## 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

Shelly is going to flip a coin 50 times and record the percentage of heads she gets. Her friend Diane is going to flip a coin 10 times and record the percentage of heads she gets. Which person is more likely to get 20% or fewer heads?

• Choose one answer.
(a) Shelly, because the greater the sample size, the greater the variability in results.
(b) Diane, because the more you flip the closer you get to 50% heads.
(c) Neither, because each flip is a separate event and the probability of heads is not affected by the number of times flipped.

### Problem 10

American males must register at a local post office when they turn 18. In addition to other information, the height of each male is obtained. The national average height for 18-year-old males is 69 inches (5 ft., 9 inches). Every day for one year, about 5 men registered at a small post office and about 50 men registered at a large post office. At the end of each day, a clerk at each post office computed and recorded the average height of the men who registered there that day.Which of the following predictions would you make regarding the number of days on which the average height for the day was more than 71 inches (5 ft., 11 inches)?

• Choose one answer.
(a) The number of days with the average heights over 71 inches would be greater for the small post office than for the large post office.
(b) The number of days with average heights over 71 inches would be greater for the large post office than for the small post office.
(c) There is no basis for predicting which post office would have the greater number of days.

### Problem 11

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 0.5
(b) Fair, because the probability of seeing that amount of heads or less is approximately 0.0013
(c) Neither fair or unfair. There is not enough information to determine that
(d) Not fair, because the probability of seeing that amount of heads or less is close to 0

### Problem 12

In craps played in American casinos, players may wager money against the casino (bank craps) on the outcome of one roll, or of a series of rolls of two dice. The sum of the two faces is the standard outcome of interest. How many outcomes constitute the sample space for the sum of the faces of one roll of two dice?

• Choose one answer.
(a) 12
(b) 6
(c) 11
(d) 36
(e) 21

### Problem 13

If two events are independent, then they are automatically mutually exclusive.

• Choose one answer.
(a) True
(b) False

### Problem 14

If two events are mutually exclusive, then the sums of their probabilities is 1.

• Choose one answer.
(a) True
(b) False

### Problem 15

The sample space of an experiment is the set of all possible outcomes of that experiment.

• Choose one answer.
(a) True
(b) False

### Problem 16

The concept of a sample space is only relevant for experiments with numerical outcomes.

• Choose one answer.
(a) True
(b) False

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