91Ó°ÊÓ

A pair of dice is rolled five times. What is the probability the first two results are "sevens" and the others are not?

Show that if event \(A\) is independent of itself, then \(P(A)=0\) or \(P(A)=1\). (This fact is key to an important "zero-one law.")

Suppose the class \(\left\\{A_{i}: 1 \leq i \leq n\right\\}\) is independent, with \(P\left(A_{i}\right)=p_{i}, 1 \leq i \leq n .\) What is the probability that at least one of the events occurs? What is the probability that none occurs?