Question

If A and B are two events, the probability of occurrence of either A or B is given as ________.
A.\[{\text{P(A) + P(B)}}\]
B.\[{\text{P(A}} \cup {\text{B) = P(A) + (B)}}\]
C.\[{\text{P(A)P(B)}}\]
D.\[{\text{P(AB)}}\]

Answer 1

Hint: In probability theory, Events \[{{\text{E}}_1},{{\text{E}}_2},\_\_\_\]En are said to be mutually exclusive if the occurrence of them implies the non-occurrence of the remaining (n-1) events. Therefore, two mutually exclusive events cannot both occur and formally said the intersection of each two of them is empty (the null events). In consequence mutually exclusive events have the property:
\[{\text{P(A}} \cap {\text{B) = E}}\]

Complete step-by-step answer:
We have given two events, Event A and Event B.
Step-I: - We have to find the probability of occurrence of either A or B. It means both events are mutually exclusive events. According to the addition theorem, if A and B due two events then probability of A union B is equal to probability of A, plus probability of B, minus probability of A intersection B.
Step-II: - Given events A and B are mutually exclusive event, so probability of A intersection B is \[{\text{{E} ie P(A}} \cap {\text{B) = {E}}}\]. So, the equation becomes \[{\text{P(A}} \cup {\text{B) = P(A) + (B)}}\]. So, if A and B are two events, then A union B refers to the occurrence of either A or B or both which means all the equally likely chances to occur in an event known as A union B.
Hence option B is correct.

Note: In logic two mutually exclusive prepositions that logically cannot be true in the same sense at the same time. To say that more than two propositions are mutually exclusive, depending on context, means that one cannot be true if the other one is true or at least one of them cannot be true.