Philosophy 210:

Practice With The

Rules Of Probability

Use the rules of probability given in class to solve the following problems. Answers are given below.

1. What are the odds that a table is not a table?

2. What are the odds that an unmarried man is a bachelor?

3. If you roll a fair 6-sided die, what are the odds that you will roll an even number?

4. Suppose that the odds of Mr. Green winning a seat in the Georgia Senate are 2/3 and the odds of Mr. Blue winning a seat in the Louisiana Senate are 1/3. What are the odds that both will win their respective elections?

5. Mr. Black and Mr. Pink are both running for the same Senate seat. The odds of Mr. Black winning are .65. What are the odds of Mr. Pink winning?

6. Suppose three people arrive at an office building with five equally accessible, randomly chosen doors. What are the odds that they all go through the same door?

7. Suppose you roll two fair 6-sided dice. What are the odds that you will roll a a total of three (that is, either a 1 and a 2, or a 2 and a 1)?

8. Suppose that the odds that Fred is a bachelor are .34. What are the odds that he is an unmarried man?

ANSWERS:

1. Zero (Rule 2).

2. One (Rule 1).

3. 1/2 (Rule 4: the three options of a 2, 4 or 6 coming up are mutually exclusive, i.e., only one of them can come up. So the odds of getting a 2, 4 or 6 are 1/6 + 1/6 + 1/6 = 3/6 = 1/2.)

4. 2/9. (Rule 6: The two race results are independent, so the odds of Green winning and Blue winning are 2/3 x 1/3 = 2/9.)

5. .35 (Rule 5: not-Mr. Black winning (i.e., Mr. Pink winning) = 1 - Mr. Black winning.

6. 1/125 (Rule 6: odds of one going through any given door are 1/5, odds of the second person going through the same door are 1/5, and the same for the third person. So 1/5 x 1/5 x 1/5 = 1/125.)

7. 2/36. (Rule 4: There are two ways to roll a "3" on two dice: you roll either 1-2 or 2-1. The odds of each is 1/36 and 1/36 + 1/36 = 2/36.)

8. .34 (Rule 3: if any two statements say the same thing, then they have the same probability.)