Question

events a and b are mutually exclusive if they can not occur simultaneously. this statement is best represented in symbols by
p(a and b)=0
a given b = 0
p(a|b)=0
a and b = 0

Explanation:

Step1: Recall probability - notation for joint events

The probability of both \(A\) and \(B\) occurring is written as \(P(A\cap B)\) (or \(P(A \text{ and } B)\)). Mutually - exclusive events have no overlap in their occurrence.

Step2: Understand the probability of non - occurring joint events

For mutually exclusive events \(A\) and \(B\), the probability that \(A\) and \(B\) occur simultaneously is 0. So \(P(A\cap B)=P(A \text{ and } B) = 0\). The notation \(P(A|B)\) is the conditional probability of \(A\) given \(B\) and \(A \text{ given } B\) is an imprecise way of writing conditional probability. \(A\) and \(B = 0\) is not a standard probability notation for the probability of the joint event.

Answer:

\(P(A \text{ and } B)=0\)