events a and b are mutually exclusive if they can not occur simultaneously. this statement is best…

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

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

Answer

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)