Question

g.pr.10.3 (lc)

which formula is the correct formula to use to test if two events are independent?

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

\\(p(a) = \frac{\text{\\# of favorable events}}{\text{total sample space}}\\)

\\(p(a \text{ and } b) = p(a) \cdot p(b)\\)

\\(p(a|b) = p(a \text{ and } b)/p(b)\\)

Explanation:

Define mathematical independence for two events

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

Evaluate the given options against the definition

$$
LATEXBLOCK0
$$

Answer:

• (A) \(P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\)
• (B) \(P(A) = \frac{\text{\# of Favorable events}}{\text{Total sample space}}\)
• (C) \(P(A \text{ and } B) = P(A) \cdot P(B)\) (Correct answer)
• (D) \(P(A|B) = P(A \text{ and } B)/P(B)\)