Question

question 10
10 pts
if a and b are overlapping events, the probability that either a or b occurs is

\\(p(a \text{ or } b) = p(a) + p(b) + p(a \text{ and } b)\\)
\\(p(a \text{ or } b) = p(a) + p(b) - p(a \text{ given } b)\\)
\\(p(a \text{ or } b) = p(a) + p(b) + p(a \text{ given } b)\\)
\\(p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)\\)

Explanation:

Identify the probability rule for overlapping events

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

Match with the given multiple-choice options

$$ \text{Option 4: } P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) $$

Answer:

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