Math 113 F99 E.

Assignment #2

Due in lecture on Friday, October 15.

We're doing §2.11 lightly. Just concentrate on distinguishing the cases and understanding the issues involved. Be able to do problems like the homework below.

§	page	NTHI	THI
§2.9	p. 37	14	12, 13
§2.10	p. 39	2, 3, 4	6, 7
§2.11	p. 45	(b) for 1 through 6	(c) for 1 through 6
§3.1	p. 86	3, 6, 8, 11, 18	7, 13, 14, 21
extra	below		E-1, E-2, E-3

Problem E-1. Bob is an extreme-sports enthusiast and does an activity for which the chance of having an accident is 1 in 100. If he does the activity 100 times, what is the chance that he will have had at least one accident?

(Give your answer as an expression and also as a number, obtained from using a suitable calculator. Think about the complementary situation: What is the chance of never having any accident?)

The following two problems caused heated controversy among the readers of the popular column of Marilyn Vos Savant¹.

Problem E-2. If a couple has exactly two children and you know that at least one of them is a boy, what is the chance that the other is also a boy? (Assume that the probabilities of boys and girls in the population are both 0.5.)

Problem E-3. The game show host Monty Hall shows the contestant three doors. A prize is behind one, at random. The contestant chooses a door. Instead of opening it right away, Monty tells the contestant one of the two remaining doors that does not have the prize, and offers the contestant a chance to change his or her original choice. Should the contestant change or not, or does it even matter?

(One approach: Imagine two contestants who do the contest repeatedly--one who always accepts the offer to change and one who never accepts. Analyze how each one does.)