Homework 1: Sample Spaces, Events, Set Theory

1. Section 1.4, #6(b), 6(d), 10.
2. An urn contains twenty-four chips, numbered 1 through 24. One is drawn at random. Let \(A\) be the event that the number is divisible by 2, and let \(B\) be the event that the number is divisible by 3. State in words, in the simplest possible way, the event represented by \(A\cap B\).
3. What must be true of the events \(A\) and \(B\) if \(A\cup B=B\)? What must be true of the events if \(A\cap B=A\)?
4. Let \(A\) and \(B\) be any two events on a sample space \(S\). Which of the following sets are necessarily subsets of which other sets: \(A\), \(B\), \(A\cup B\), \(A\cap B\), \(A^c\cap B\), \(A\cap B^c\), \((A^c\cup B^c)^c\)?