Assignment6

for the weeks beginning October 16

# Instructions

By Wednesday, October 11:

·         Read Chapter 8 of TTT, through page 206.

By Wednesday, October 18:

If you have not had calculus or are not comfortable with it, don’t worry about the mathematical details of the argument on pages 207-209. But make sure you understand the goal of the calculation, expressed at the top of page 208, and Price’s conclusion, described at the bottom of page 209.

Turn in the homework assignment at the beginning of class on Monday, November 6.

# Homework assignment

1.     Suppose I roll two dice, one red and one green. Then there are 36 possible outcomes; for example, <1,5> represents the outcome that the red die reads 1 and the green die reads 5. Assume each of these outcomes is equally likely. Then for each of the events listed below, list the outcomes which constitute the event (for example, event A is the set {<5,6>, <6,5>}), and then determine the probability that the event occurs.

a)       Event A: The sum of the two dice is 11.

b)       Event B: The sum of the two dice is 9.

c)       Event C: The sum of the two dice is at least 8.

d)       Event D: The red die reads 6

e)       Event E: The green die reads 6

f)        Event F: Both dice read 6

g)       Event G: At least one die reads 6

h)       Event H: The sum of the two dice is even.

2.     As in problem 1, list the outcomes which constitute the event, and determine the probability that the event occurs.

1.        The union of events A and B

2.        The union of events A and D

3.        The intersection of events C and D

4.        The intersection of events D and H

5.        The complement of event D

3.     Are events A and B incompatible? What about A and D? Explain.

4.     Are events C and D independent? What about D and H? Explain.

5.     I draw a marble from an urn with 200 red marbles and 300 blue marbles; and then replace it, and repeat the process four more times. What are the odds that in the end I will have chosen a red marble exactly three times?

# Thought questions

1.        What is the distinction that Hume makes between “demonstrative reasoning” and “moral reasoning” in Section IV, Part II, of his Enquiry? (M)

2.        At the end of Section IV, Part II, Hume explains that he has tried to show that “it is not reasoning which engages us to suppose the past resembling the future, and to expect similar effects from causes, which are, to appearance, similar.” Outline the arguments that Hume has presented to make the case. (L)

3.        How does Berkeley’s views on matter, and his criticism of calculus, support a belief in God?

4.        Discuss the features that are common to the epistemological views of Locke, Berkeley, and Hume.