Question

a student is not sure when to add and when to multiply probabilities. how do your respond?
choose the correct answer below.
a. one multiplies probabilities when events are independent. adding probabilities occurs when separate outcomes are a part of the desired event.
b. one multiplies probabilities when events are mutually exclusive. adding probabilities occurs when events are dependent.
c. one multiplies probabilities when events are mutually exclusive. adding probabilities occurs when events are independent.
d. one multiplies probabilities when separate outcomes are a part of the desired event. adding probabilities occurs when events are independent.

Explanation:

To determine when to add or multiply probabilities, recall the rules:

• Independent Events: The probability of both occurring is the product of their individual probabilities (multiplication rule: \( P(A \cap B) = P(A) \times P(B) \) for independent \( A, B \)).
• Mutually Exclusive Events: The probability of either occurring is the sum of their individual probabilities (addition rule: \( P(A \cup B) = P(A) + P(B) \) for exclusive \( A, B \), meaning they cannot happen simultaneously).

Now analyze the options:

• Option A: Matches the rules. Multiplying for independent events (both can occur), adding for mutually exclusive (either/or, separate outcomes of the desired event).
• Option B: Incorrect. Mutually exclusive events use addition, not multiplication; dependent events do not follow the "multiply for exclusive" logic.
• Option C: Incorrect. Mutually exclusive events use addition, independent events use multiplication (reverse of what’s stated).
• Option D: Incorrect. The logic for multiplication (separate outcomes) and addition (independent) is reversed.

Answer:

A. One multiplies probabilities when events are independent. Adding probabilities occurs when separate outcomes are a part of the desired event.