Multiplication theorem of probability is applicable for :Group of answer choicesIndependent eventsMutually exclusive eventsConditional eventsExhaustive events

The multiplication theorem of probability is applicable for independent events.

Here's a step-by-step explanation:

1. Understanding the Multiplication Theorem of Probability:

   • The multiplication theorem of probability states that for two independent events, the probability of both events occurring together (i.e., the intersection of the two events) is the product of their individual probabilities.

2. Definition of Independent Events:

   • Two events are considered independent if the occurrence of one event does not affect the occurrence of the other event. In other words, the probability of one event happening remains unchanged regardless of whether the other event happens or not.

3. Mathematical Representation:

   • If $A$ and $B$ are two independent events, then the probability of both $A$ and $B$ occurring is given by: $P(A \cap B) = P(A) \times P(B)$

4. Application to Other Types of Events:

   • Mutually Exclusive Events: These are events that cannot occur simultaneously. For mutually exclusive events $A$ and $B$, $P(A \cap B) = 0$, so the multiplication theorem does not apply.
   • Conditional Events: These are events where the probability of one event depends on the occurrence of another event. The multiplication theorem for conditional events is different and involves conditional probabilities.
   • Exhaustive Events: These are events that cover all possible outcomes of an experiment. The multiplication theorem is not specifically related to exhaustive events.

Therefore, the correct answer is independent events.