Practice Questions

Here are some sample test questions for for Chapter 6 and Bayes' Theorem, with review topics in parentheses. On an actual test, I will not put anything in parentheses about the topic. You are supposed to figure that out.

- (sample space)
If R is the measure of an earthquake on the Richter scale, then of the following sample spaces for R, which one(s) would be considered valid? For ones that you do not think are valid, briefly explain why not.

a) {0 < R <= 2, 2 < R <= 6, 6 < R}

b) {0 < R <= 4, 3 < R <= 6, 6 < R}

c) {1,2,3,4,5,6,7,8,9} - (multiplication rule for independent events)
In the dice game craps, each throw consists of rolling two dice and taking their sum. You win on the first throw if you get a 7 or 11. Big Julie from Chicago brings his own dice to a game and wins on his first throw four times in a row. What is the probability of this happening with fair dice?

- (contingency tables)
A magazine asked some women aged 55 or older whether they thought their husbands needed Rogaine or Viagra. 50 percent said that they thought that their husbands needed Rogaine. 20 percent said that they thought that their husbands needed Viagra. 5 percent thought that they needed both.

Are the need for Rogaine and the need for Viagra independent, related positively, or related negatively? Justify your answer.

- (Pascal's triangle)
The World Tiddlywinks Championship is a best of 9 series, with the first team to win five games taking the trophy. Suppose that the finalists, MIT and Cal Tech, are evenly matched, so for each game MIT has a .5 probability of winning. What is the probability that after five games MIT will be up 3 games to 2?