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Assignment 2
This assignment should take you approximately six hours to complete. It consists of twelve questions. The value of each question is indicated by the question. The answers required for this assignment require you to respond in a longer fashion (approx. 2-3 paragraphs) nonetheless be concise and approach each question directly. If the question asks for an explanation with your answer, then the quality of that explanation counts in your mark for the question. The total possible high mark for this assignment is 100 marks.Argument from Analogy Questions 1 – 3: (10 marks each) Consider the following three arguments from analogy. For each argument, indicate the entities between which the similarity is being drawn. For each argument, assess whether the argument is strong or weak. Explain your assessment.
1. Almost everyone would throw a life preserver to a drowning person; indeed, someone who could easily do so but refused would be regarded by everyone as a sick or immoral person. The same thing applies to nations when a famine occurs in a Third World country. We should be prepared to throw them a life preserver in the form of emergency aid. Yet, we continually hear complaints from those who are opposed to such aid. Surely we are entitled to regard them as sick or immoral people.
2. England and Japan have much lower overall crime rates than the United States. The United States has 20 times more homicides than England and 30 times more than Japan. All three countries have large populations, are highly industrialized, and are in the top five in economic strength among the world’s countries. In addition, all three countries are democracies, have separate branches of government, and a large prison system. But England and Japan have strict gun control legislation. If the United States wants to lower its homicide rate, then it has to pass strict gun control legislation.
3. George is anticipating the purchase of a new flat screen TV, and he notices that his friend Kramer’s new Toshiba flat screen TV gets the finest picture he has ever seen. George concludes that if he buys a Toshiba flat screen TV, his flat screen TV will get approximately the same picture quality as Kramer’s.
Statistical Reasoning Questions 4-5: (10 marks each) In each of the following passages, identify the sample and the population. Next, indicate whether the sample is representative of the population referred to in the conclusion in the passage. Analyze for sample size, potential bias and randomness. Determine the strength of the argument being presented in the passage.
4. I am never going to buy another Baxter car again. I had one and so did my brother. Both our cars were constantly in the shop. They had electrical and carburetor problems that caused them to stall all the time with no warning. Then we would have to get them towed, because they wouldn’t start again. I am sure that all Baxter cars have the same kind of problems; that is why I won’t buy another one no matter what the price.
5. From 1903 to 2008 whenever the American League won the baseball World Series, cigarette sales rose 20% over the previous year. But when the national league won the baseball World Series, liquor sales rose 25% for the next year. Stock buyers pay heed! Watch who wins the baseball World Series, and then buy or sell accordingly.
Probability Questions 6-9: (5 marks each) Calculate the probability for each of the following scenarios. Show your work, and explain your choice of formula used to derive your answer.
6. A standard deck of 52 playing cards containing two red queens and two black queens is thoroughly shuffled. Determine the probability of picking one card at random and getting a black queen.
7. Determine the probability that two people randomly chosen will both be born on the same day of the week.
8. Imagine a box of 15 CDs contains these types of music: four jazz CDs, four classical CDs, three rap CDs, three reggae CDs, and one disco DC. If two CDs are randomly drawn, but the first CD is put back into the box before the second is picked, determine the probability that both CDs will be jazz.
9. Suppose you have a drawer of socks in these colours and amounts:
three black socks
four white socks
four brown socks
three orange socks
one red sock
If you draw two socks in succession, without replacing the first before the second draw, then what is the probability that both socks will be brown?
Causal Arguments Questions 10-11: (10 marks each) In the following passages explain which of Mill’s Methods applies and determine the conclusion that can be derived from that method. For each passage, indicate whether the intended causality is characterized as a sufficient condition, a necessary condition, both a sufficient and a necessary condition, or neither.
10. Tom and Marsha both bought new cars. They chose the same make and model, with the same size engine and automatic transmission and same tire size. They both buy their gas at the same station and use the same octane gas. Tom drives his car exclusively in the city, while Marsha does mainly highway driving. However, when they compared gas mileage, Marsha’s car averages 35 miles per gallon (MPG), but Tom’s car averages only 26 MPG.
11. Steve had $250 in his wallet on Friday afternoon. By Sunday night he had only $10 left. He recalled spending $60 on a dinner and a date Friday night. Then he spent $70 on groceries, $40 on gas for his car, and lent $50 to a friend. He didn’t recall spending any more money, so the only thing he could think of was that he must have lost the $20 somewhere.
12. Hypothetical Reasoning Question: (10 marks) The following passage contains an example of hypothetical reasoning. Identify the hypothesis being proposed. Also state some observable predictions that would follow from the hypothesis. Finally, provide an alternate hypothesis that you believe provides a better explanation for what has been observed. Explain why your hypothesis is better.
You oversleep and concerned about missing an appointment, so you dress hurriedly, skip breakfast, and leave the house as quickly as you can. When you return home in the evening, you find the front door ajar. When you go inside, nothing is disturbed. The house is exactly as you left it in the morning. You infer a burglar who was scared off before stealing anything is responsible.
This assignment contains some questions from some of the following:
1. Baronett, Stan. Logic Second Edition. OUP. (New York: 2013) ISBN 978-0-19-984631-3.
2. Flage, Daniel E.. Understanding Logic. Prentice-Hall. (Englewood Cliffs New Jersey: 1995) ISBN 0-02-338173-6
3. Salmon, Merrilee H.. Introduction to Logic and Critical Thinking Third Edition. Harcourt Brace & Company. (Fort Worth: 1995) ISBN 0-15-543064-5
| Subject | Uncategorized | Pages | 11 | Style | APA |
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Answer
- - Someone is to Everyone as ‘Some people’ is to ‘We’.
- Someone is sick or immoral to everyone
- It is probable that ‘Some people’ is sick or immoral to ‘We’.
In this case, entities Someone and Everyone are related in the analogue case while ‘Some people’ and ‘We’ are related in the subject case. Sick or Immoral is the subject feature specified to describe entities in the analogue case. On the analogy basis, there are probable grounds to infer that the subject feature also describes relation between entities in the subject case. This is an argument case by relation.
Since there is a relevant similarity between ‘Everyone’ and ‘We’, the argument is strong. This is also based on the fact that there are no relevant dissimilarities.
- - England, Japan and the US have large populations, are highly industrialized, and are in the top five in economic strength among the world’s countries, are democracies, have separate branches of government, and a large prison system.
- England and Japan have much lower overall crime rates than the United States, and have strict gun control legislation.
- Therefore, the US would have lower homicide (crime) rates if it had as strict gun control policies.
Due to the high number of entities in the analogue case, the argument probability is made strong. The argument has six relevant similarities and two relevant dissimilarity. Therefore, the argument is strong. It is strongly probable that strict gun control policies would reduce homicide rates in the United States.
- – Kramer has new Toshiba flat screen TV with good quality pictures.
- Therefore, George infers that in getting a similar TV he will get similar results.
George’s inference of acquiring a similar Toshiba TV for the high quality pictures is modest and therefore very probable. The argument is strong, since it includes both the product and the manufacturer which are very relevant similarities. Further, George’s argument is not bold since his expectations of high quality pictures was not exceeding the analogue case for Kramer. Therefore, George’s inference is largely supported by the evidence he has.
- The sample size is 2, while the population is of those who have used Baxter cars
The sample is too small to conclusively replicate properties of the population and therefore, does not represent the population. Therefore, it is not consistent to conclude from the sample that Baxter cars have the same kind of problems as described.
Since the argument is not randomized, it is highly biased in the conclusion.
Therefore, the argument in the conclusion is too weak to hold based on the sample size and selection criteria. Since the sample size does not represent the population of those who have used Baxter cars, the conclusion based on it does not have sufficient backing of evidence.
- The two samples are independent. The first sample is drawn from the population of cigarette buyers while the second is from population of liquor buyers.
Since the research type is a census, the conclusion is based on the entire population as all-inclusive in both cases as total sales are considered in the statistical thinking. The thinking is not based on a portion of the population (sample) but on the entire population and so is not representative.
Therefore, the results in not biased and the inference is consistent since it is tested over a wide time horizon of from 1903 to 2008.
- S = 52
q (red queen) = 2
P(q) = q/S = 2/52 = 1/26
A single card has a 1/52 chance of being picked in a single random draw. In the random sample, there are 2 black queens where each has a chance of being deawn from the deck in the single picking.
Therefore, the outcome probability of picking a black queen card is based on the possible outcome of either of the back queens ( say Black queen card 1 or black queen card 2). This means that the outcome is formulated by adding the event possibilities of the 2 black queen cards, i.e. 1/52 + 1/52.
The probability of picking one card at random and getting a black queen from the standard deck of 52 playing cards is 1/26.
- S = 7
P (being born in any day of the year) = 7/7
P (bring born on a specific day of the year) = 1/7
P (2 people being born on the same day of the year) = (7/7) × (1/7)
= 1/7.
This is based on the reasoning that one person can be born on any day of the week so there is a possibility of the entire probability space, probability of 1 or 7/7.
The second person, however, has to be born on the specific day as the first person and so has a probability of 1/7.
A combined probability of the two is found by multiplication of the two probabilities since the probability outcome is based on the event 1 (first person’s birthday) AND event 2 (second’s person’s birthday similar to the first person’s).
Therefore, the probability that two people randomly chosen will both be born on the same day of the week is 1/7.
- S = 15
Jazz (j) = 4
Classical (c) = 4
Rap (r) = 3
Reggae (g) = 3
Disco (d) = 1
P (j) = 1/15 + 1/15 + 1/15 + 1/15 = 4/15
P (j and j) = 4/15 × 4/15
= 16/225
The probability of picking a single CD from the probability space is 1/15.
But there are 4 jazz CDs in the box of 15, so the probability of picking a Jazz CD in a single picking event is the probability of picking either of the 4 Jazz CDs, therefore the outcome probability is 4/15.
But the event of picking is repeated with replacement. This means that the two events are independent and so the probability of picking a Jazz CD in the first event is similar to the probability of picking a jazz CD in the second event.
The overall outcome probability of picking two Jazz CDs in the two attempts of picking is 16/225.
- S = 15
Black (b) = 3
White (w) = 4
Brown (n) = 4
Orange (o) = 3
Red (r) = 1
The probability of drawing one brown socks in the first draw is
P (n) = 1/15 + 1/15 + 1/15 + 1/15 = 4/15
In the case that the first sock has been drawn and is brown, drawing the second socks on an event without replacement means that the number of brown socks has reduced by 1 (there is remaining in the box 3 brown socks) and the probability space has also reduced to 14. Therefore the probability for drawing the second brown socks is as follows:
P (n-1) = 1/14 + 1/14 + 1/14 = 3/14
Therefore, the probability of drawing two brown socks from the box without replacement is:
P (n and n-1) = 4/15 * 3/14
= 12/ 210 = 6/105
Therefore, the probability that both socks will be brown when two socks are drawn from the box in succession without replacement is 6/105.
- The Method of difference is used. Driving place is the difference (City for Tom and highway for Marsha) since all the other factors are similar for both of the two. It is therefore plausible to conclude that highway driving increases gas mileage.
The causality in this case is a necessary condition since driving place affects mileage. That is, if highway driving then high mileage and if city driving then low mileage. This can be based on the facts like type of roads in the cities which at times include rough road driving, many stops, waits on traffic, low speeds, and many other factors as compared to the free high speed driving in the good highway roads. The causality is a good argument.
- Steve uses the Joint Method to conclude that he must have lost $20. Since he uses the method of agreement to trace is spending of the $250 and uses the method of difference to allocate causality for the $20 unaccounted for, he employs the Mill’s Joint method. Steve looks at antecedent circumstances and finds that the factors agree, as he can account for the money $230 of the $250. Then he uses method of difference to establish a causality for the $20 and coins a plausible circumstance that since he cannot account for the money then he must have lost the $20 somewhere.
This argument is not good since there are other factors that could be considered, including refreshing memory if in case there is an antecedent circumstance he forgets. The intended causality, therefore, cannot be characterized as either necessary or sufficient condition since the plausible cause is not good enough to indicate a causality relation. In this sense, it is impossible to establish a causality characterization that whenever money cannot be accounted for then it is lost somewhere, nor is it plausible to claim that money unaccounted for has to be lost and nothing more.
- The hypothesis proposed is that a burglar who was scared off before stealing anything is responsible for the door that was ajar.
This thought is based on the front door being ajar, something which has never happened before or is quite uncommon in my case. The possibility of a burglar breaking into the house and being scared off by my encroachment before stealing anything is based on the fact that everything was intact in in spite of the fact that the door was ajar which creates a first impression of intrusion.
The alternative hypothesis in this case is that in a hurry I left the door ajar.
The alternative hypothesis is better based on two fundamental reasons. First, I overslept when there was an important appointment to meet and so woke up and hurried to prepare for the appointment and left hurriedly (this is indicated by other observable predictions like dressing hurriedly, skipping breakfast and leaving the house as quickly as possible). This inference is a better argument than the first based on the observable indicator evidences. Secondly, the possibility of a burglar taking time to break into the house and leaving without anything is a bad argument in the sense that it is not a sensible inference. It is not reasonably plausible that the burglar might have been scared off by my encroachment and left ran away through the front unnoticed. Therefore, the alternative hypothesis is a better explanation of the condition than the original hypothesis.
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