Back to Understand independence via the product rule — Problem 3 · Task Set 19

Exercises: Understand Independence Through the Product Rule

Work through each section in order. For independence tests, compute $P(A)$ , $P(B)$ , and $P(A \text{ and } B)$ , then compare $P(A \text{ and } B)$ to the product $P(A) \cdot P(B)$ . For explanation problems, write in complete sentences.

Grade 10·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-cp-a-2

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Warm-Up: Probability Foundations

These problems review skills you already know.

Two events $A$ and $B$ are mutually exclusive when they cannot both occur. What is $P(A \text{ and } B)$ for mutually exclusive events?

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

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

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

$P(A \text{ and } B) = 1$