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 the Question:
We need to name the relationship between two events where one event's outcome does not change the probability of the other.

Step 2: Key Concept:
In probability, events are classified by whether knowing one outcome changes your expectation of the other. If it does not change anything, the events are independent.

Step 3: Detailed Explanation:
For two independent events \( A \) and \( B \), the joint probability simply multiplies: \[ P(A \cap B) = P(A) \cdot P(B) \]
This multiplication only works because neither event's chance of happening shifts based on the other one occurring.
Dependent events break this rule, since one event changes the odds of the other. Mutually exclusive events describe a different idea entirely, they cannot occur together at all, which is not the same as being unaffected by each other.

Step 4: Final Answer:
Two events unaffected by each other's outcome are called independent events.