**QUESTION**

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

**Argument from Analogy Questions 1 – 3:**** **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:**** **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:**** **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:**** **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: **** **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, like all the assignments and term exams for this section of PHIL 1320, 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*

*4. Warmbrod, Ken. *__Logic and Philosophy of Logic Course Guide for Philosophy 2430.__* University of Manitoba. (Winnipeg: 2013) ISBN 978-0-200-00202-8 *

A**NSWER**

**Ans.1) **

** **Similarities : 1) Entity : Life Preserver: Both the person and the famine would throw a life preserver.

2) Entity : Sick or Immoral: Someone who could easily do so but refused and people who continuously complain about opposing to such aid are sick or immoral.

Assesment : Argument is strong.

**Ans.2) **

** **Ans) Similarities: 1) Entity : Population: All 3 countries have large Population.

2) Entity : Industrialization : All 3 countries are highly industrialized.

3) Entity : Economic Strength : All are in top 5.

4) Entity : Democracies : All 3 are Democracies and have separate branches of government.

5) Entity : Prison System : All 3 have large Prison System.

Dissimilarities : 1) Entity : Crime rate

2) Entity : Homicides

3) Entity : Gun Control Legislation

Assessment : Argument is strong.

**Ans.3) **

** **Similarities: 1) Entity : Tv : Both are flat tv

Dissimilarities : 1) Entity : Picture Quality : Toshiba flat Tv has finest.

Assessment : Argument is weak.

**Ans.4) **

Using these study results, construct a 95% confidence interval for the difference in the proportion of

Buying all Baxter cars.

First, compute the sample proportions:

P^shared – P^notshared = sample proportions.

Bias in sampling is the tendency for samples to differ from the corresponding population in some systematic way. Bias can result from the way in which the sample is selected or from the way in which information is obtained once the sample has been chosen.

Also we can use, Stratified Random Sampling When the entire population can be divided into a set of nonoverlapping subgroups, a method known as stratified sampling often proves easier to implement and more cost-effective than simple random sampling.

**Q5=Ans) **

When an experiment can be viewed as a sequence of trials, randomization involves the random assignment of treatments to trials. Remember that random assignment— either of subjects to treatments or of treatments to trials—is a critical component of a good experiment. Randomization can be effective only if the number of subjects or observations in each treatment or experimental condition is large enough for each experimental group to reliably reflect variability in the population. For example, if there were only eight students requesting calculus, it is unlikely that we would get equivalent groups for comparison, even with random assignment to the four sections. Since 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. Therefore, When the entire population can be divided into a set of nonoverlapping subgroups, a method known as stratified sampling often proves easier to implement and more cost-effective than simple random sampling.

**Q6.Ans) **

P(Black) = 26/52 or ½ , P(Queen) is 4/52 or 1/13 so P(Black and Queen) = ½ * 1/13 = 1/26

**Q.7.Ans)**

1/7

Explanation: It doesn’t matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7.

**Q.8.Ans)**

Since the both CD will be jazz, the events are mutually exclusive. P(jazz) = 4/15 number of jazz CDs total number of CDs P(classical) = 4/15 number of rap CDs total number of CDs P (jazz or classical) = P(jazz) + P(classical) Definition of mutually exclusive events = 4/15 + 4/15 Substitution. = 8/15 Add. The probability of choosing both the jazz is 8/15.

**Q.9)**

The correct answer is: 2/35.

References: Let *A* be the event of drawing a brown sock on the first attempt. The probability, *P(A)*, of this occurring is 4/15. Now *if A* occurs, then there will be only fourteen socks left in the drawer, three of which will be brown (because one brown sock has been removed). The probability of getting a brown sock on the second attempt, called *B*, is 3/14. We calculate the probability of getting two brown socks in succession as the joint occurrence of *A* and ( *B* if *A*), which is the product of the probabilities of their separate occurrence: 4/15 x 3/14 = 12/210. Dividing both by 6, we get 2/35.

**Q.10)**

**Ans**

Causal arguments are inductive arguments that seek to establish a causal relationship.

Causal arguments look to an effect or a cause and seek to connect them to a general rule of cause and effect. An example of a causal argument is to claim that smoke always follows from a fire, so therefore fire is the cause of the smoke. Causal arguments are evaluated on strength and weakness depending on how many cases are studied and what sorts of controls are applied to rule out alternative explanations for the proposed causal relationship.

Here,

Tom and Masha bought same car because the cause is they have same size engine and automatic transmission and same tire size.

Also, , Marsha’s car averages 35 miles per gallon (MPG), but Tom’s car averages only 26 MPG.

Cause: . Tom drives his car exclusively in the city, while Marsha does mainly highway driving.

**Q.11)**

Ans: Steve must have lost the $20 somewhere.

Cause: 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. And might have lost 20 dollar somewhere.

**Q.12)**

Ans)

You oversleep and concerned about missing an appointment, so you dress hurriedly, skip breakfast, and leave the house as quickly as you can. Even if you were in hurry all the items in the house is undisturbed and everything was exactly in the same position as you left in the morning.

So,the argument is valid.

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