Problem 1

Give a rigorous mathematical proof of:

\[ A \cup (B \cap A^c)=A \cup B\]

Problem 2

Give a mathematically correct proof of Boole’s inequality

Problem 3

A box contains 20 blue balls and 10 green balls. Define appropriate sample spaces and events and use them to find

1. the probability to select a blue ball from the box.

2. the probability to select (in one move) a blue ball and a green ball.