Question

question 5
10 pts
for non-overlapping events a and b, which probability formula is correct?
\\( p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b) \\)
\\( p(a \text{ or } b) = p(a) \times p(b) \\)
\\( p(a \text{ or } b) = p(a) - p(b) \\)
\\( p(a \text{ or } b) = p(a) + p(b) \\)

Explanation:

Define non-overlapping events

Non-overlapping (mutually exclusive) events cannot occur simultaneously:

$$ P(A \text{ and } B) = 0 $$

Apply the general addition rule

The general addition rule for any two events is:

$$ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) $$

Simplify for non-overlapping events

Substituting \(P(A \text{ and } B) = 0\) into the general formula:

$$ P(A \text{ or } B) = P(A) + P(B) $$

Answer:

• (A) \(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\)
• (B) \(P(A \text{ or } B) = P(A) \times P(B)\)
• (C) \(P(A \text{ or } B) = P(A) - P(B)\)
• (D) \(P(A \text{ or } B) = P(A) + P(B)\) (Correct answer)