Phil

Exam 2

Phil/Leap 1250

1 Question 1

Using Venn diagrams, test the following syllogistic forms for validity: #1. All M is P All M is S ———- All S is P

#2. Some M is P Some M is not S ———- Some S is not P

#3. Some P is M Some S is not M ———- Some S is P

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2 Question 2

What does it mean for two propositions to be statistically independent? Answer this question by giving both (i) a formal, probabilistic definition, and (ii) a more intuitive definition in your own words.

3 Question 3

What does it mean for two propositions to be mutually exclusive? Answer this question by giving both (i) a formal, probabilistic definition, and (ii) a more intuitive definition in your own words.

4 Question 4

Can two propositions be both mutually exclusive and independent? Explain your answer.

5 Question 5

What is the probability of drawing a King from a standard fifty-two-card deck, and then (after replacing the King to the deck and reshuffling) drawing another King?

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6 Question 6

If you roll two fair six-sided dice one time, what is the probability that one or the other (or both) of the dice will come up a five?

7 Question 7

Jim, a famous baseball player, tests positive for steriod use in a random screening of all major leaguers. It is known that the test used has a ”true positive” rate (the probability that the test will be positive given that the person does indeed use steroids) of 95% and a ”false positive” rate (the probability that the test will be positive given that the person does not use sterioids) of 10%. Moreover, it is also known that 10% of major leaguers are steroid users. What is the probability that Jim really does use steroids given that he tested positive?

8 Question 8

When reasoners judge that a conjunction is more probable than one of its corresponding conjuncts, they are

committing a fallacy. Provide a formal explanation (in terms of probability theory) and an informal explanation

in your own words.

9 Question 9

Only one of the following statements is true. Which one? A. Every argument that has all true premises and a true conclusion is valid. B. Every argument that has false premises is invalid. C. Every argument that has all true premises and a false conclusion is invalid. D. All of the above statements are actually false.

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10 Question 10

Using a truth-table, test the following argument form for validity: #1. p v q p ⊃ q q ⊃ r ———- r

#2. (p ⊃ q)&(p ⊃ ¬r) q&r ———-¬p

#3. r ———- (p ⊃ q) v (q ⊃ p)

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