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Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic

Walter Sinnott-Armstrong, Robert J. Fogelin

Chapter 11

Chances - all with Video Answers

Educators

Chapter Questions

06:29

Problem 1

Using the above chart, answer the following questions about the total on throw of two dice:
1. What is the probability of throwing a five?
2. Which number has the highest probability of being thrown? What is its probability?
3. What is the probability of throwing an eleven?
4. What is the probability of throwing either a seven or an eleven?
5. Which is more likely: throwing either a five or an eight?
6. Which is more likely: throwing a five or an eight, or throwing a two or a seven?
7. What is the probability of throwing a ten or above?
8. What is the probability of throwing an even number?
9. What is the probability of throwing an odd number?
10. What is the probability of throwing a value from four to six?
11. What is the probability of throwing either a two or a twelve?
12. What is the probability of throwing a value from two to twelve?

Charles Carter
Charles Carter
Numerade Educator
09:28

Problem 2

Use the rules of probability to calculate these probabilities:
1. What is the probability of rolling a five on one throw of a fair six-sided die?
2. What is the probability of not rolling a five on one throw of a fair six-sided die?
3. If you roll a five on your first throw of a fair six-sided die, what is probability of rolling another five on a second throw of that die?
4. If you roll two fair six-sided dice one time, what are the chances that both of the dice will come up a five?
5. If you roll two fair six-sided dice one time, what are the chances that one or the other (or both) of the dice will come up a five?
6. If you roll two fair six-sided dice one time, what are the chances that one and only one of the dice will come up a five?
7. If you roll two fair six-sided dice one time, what are the chances that at least one of the dice will come up a five?
8. If you roll two fair six-sided dice one time, what are the chances that at least one of the dice will not come up a five?
9. If you roll six fair six-sided dice one time, what are the chances that at least one of the dice will come up a five?
10. If you roll six fair six-sided dice one time, what are the chances that at least one of the dice will not come up a five?

Julian Wong
Julian Wong
Numerade Educator
08:27

Problem 3

Compute the probability of making the following draws from a standard fiftytwo-card deck:
1. Drawing either a seven or a five on a single draw.
2. Drawing neither a seven nor a five on a single draw.
3. Drawing a seven and then, without returning the first card to the deck, drawing a five on the next draw.
4. Same as 3, but the first card is returned to the deck and the deck is shuffled after the first draw.
5. Drawing at least one spade in a series of three consecutive draws, when the card drawn is not returned to the deck.
6. Drawing at least one spade in a series of four consecutive draws, when the card drawn is not returned to the deck.
7. Same as 6 , but the card is returned to the deck after each draw and the deck is reshuffled.
8. Drawing a heart and a diamond in that order in two consecutive draws, when the first card is returned to the deck and the deck is reshuffled the first draw.
9. Drawing a heart and a diamond in any order in two consecutive draws, when the first card is returned to the deck and the deck is reshuffled the first draw.
10. Drawing a heart and a diamond in any order in two consecutive draws, when the first card is not returned to the deck after the first draw.

Derek Follett
Derek Follett
Numerade Educator
01:18

Problem 4

Suppose there are two little lotteries in town, each of which sells exactly one hundred tickets.
1. If each lottery has only one winning ticket, and you buy two tickets to the same lottery, what is the probability that you will have a winning ticket?
2. If each lottery has only one winning ticket, and you buy one ticket to each of the two lotteries, what is the probability that you will have at least one winning ticket?
3. If each lottery has only one winning ticket, and you buy one ticket to each of the two lotteries, what is the probability that you will have two winning tickets?
4. If each lottery has two winning tickets, and you buy one ticket to each of the two lotteries, what is the probability that you will have at least one winning ticket?
5. If each lottery has two winning tickets, and you buy two tickets to the same lottery, what is the probability that you will have two winning tickets?
6. If each lottery has two winning tickets, and you buy two tickets to the same lottery, what is the probability that you will have at least one winning ticket?

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator
03:30

Problem 5

1. You are presented with two bags, one containing two ham sandwiches and the other containing a ham sandwich and a cheese sandwich. You reach in one bag and draw out a ham sandwich. What is the probability that the other sandwich in the bag is also a ham sandwich?
2. You are presented with three bags: two contain a chicken-fat sandwich and one contains a cheese sandwich. You are asked to guess which bag contains the cheese sandwich. You do so, and the bag you selected is set aside. (You obviously have one chance in three of guessing correctly.) From the two remaining bags, one containing a chicken-fat sandwich is then removed. You are now given the opportunity to switch your selection to the remaining bag. Will such a switch increase, decrease, or leave unaffected your chances of correctly ending up with the bag with the cheese sandwich in it?

Wendi Obritz
Wendi Obritz
Numerade Educator
01:27

Problem 6

Construct tables to confirm these calculations of $\operatorname{Pr}(h \mid e)$ for base rates of 0.03 and 0.3 .

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:54

Problem 7

Construct tables to confirm the above calculations of probabilities after a second and third positive test result.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
04:30

Problem 8

1. What would Wendy's chances of having colon cancer be if the other probabilities remained the same as in the original example, except that the probability that a person in the general population has colon cancer only 0.1 percent (or 0.001 )?
2. What would Wendy's chances of having colon cancer be if the other probabilities remained the same as in the original example, except that the probability that a person in the general population has colon cancer 1 percent $(0.01) ?$
3. What would Wendy's chances of having colon cancer be if the other probabilities remained the same as in the original example, except that the conditional probability that the test is positive, given that the patient has colon cancer, is only 50 percent (or 0.5 )?
4. What would Wendy's chances of having colon cancer be if the other probabilities remained the same as in the original example, except that the conditional probability that the test is positive, given that the patient has colon cancer, is 99 percent (or 0.99)?

Haggai Liu
Haggai Liu
Numerade Educator