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Back to Understand independence via the product rule — Problem 2 · Task Set 19

Exercises: Understand Independence Through the Product Rule

Work through each section in order. For independence tests, compute P(A)P(A), P(B)P(B), and P(A and B)P(A \text{ and } B), then compare P(A and B)P(A \text{ and } B) to the product P(A)⋅P(B)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
Work through problems with immediate feedback
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Fluency Practice

Test each pair of events using the product rule.

1.

A fair die is rolled once. Let $A = $ "even" ={2,4,6}= \{2, 4, 6\} and $B = $ "greater than 2" ={3,4,5,6}= \{3, 4, 5, 6\}. Compute P(A and B)P(A \text{ and } B) directly by counting the outcomes in both events. Express your answer as a fraction.