theory of probability 1

MATH 464

HOMEWORK 1

SPRING 2013

The following assignment is to be turned in on Thursday, January 24th, 2013.

1. Let A, B, and C be events (subsets) of a sample space Ω. Write each of the following events in terms of A, B, and C using intersec- tions, unions, and complements.

(a) None of A, B, C occurs. (b) At least two of A, B, C occur. (c) Exactly one of A, B, C occurs. (d) Exactly two of A, B, C occur. (e) Exactly three of A, B, C occur. Hint: Read Section 1.2 of the book.

2. Do exercises 3, 5, and 6 on pages 5 and 7 of the book.

3. Consider an unfair coin which has probability 1/3 for heads and 2/3 for tails. Do an experiment where you flip this coin until you get heads and stop. (a) Write out a simple sample space. (b) What is the probability it takes exactly 5 flips? (c) What is the probability it takes at least 3 flips?

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