Question

If one event is unaffected by the outcome of another event, the two events are said to be:

• A. Mutually exclusive
• B. Dependent
• C. Either dependent or independent
• D. Independent

Hint:

Independent events are defined by the fact that their probabilities remain unaffected by each other. Remember, \( P(A \cap B) = P(A) \cdot P(B) \) for independence.

Answer 1

The Correct Option is D

Step 1: Understanding independent events. Two events are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other. Mathematically, for two independent events \( A \) and \( B \): \[ P(A \cap B) = P(A) \cdot P(B) \] 

Step 2: Explanation of incorrect options. 
- (A) Mutually exclusive: Mutually exclusive events cannot occur simultaneously. If one event occurs, the other cannot, making them dependent in a way. 
- (B) Dependent: Dependent events are those where the occurrence of one event affects the occurrence of the other. 
- (C) Either dependent or independent: This is ambiguous and does not define the relationship clearly.