Back to Conditional Probability and the Rules of Probability — Problem 2 · Task Set 35

HSS.CP Tutor Intake - Events, Independence, Conditional Probability, and the Rules of Probability

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Grade 11·10 problems·~14 min·Common Core Math - HS Statistics and Probability·domain·cp

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Procedures

For events $A$ and $B$ , $P(A) = 0.5$ , $P(B) = 0.4$ , and
$P(A \cap B) = 0.2$ . Are $A$ and $B$ independent, and why?

Yes - $P(A) \cdot P(B) = 0.2$ , which equals $P(A \cap B)$ .

No - $P(A) + P(B) = 0.9$ , which is not equal to $P(A \cap B)$ .

No - independent events must have $P(A \cap B) = 0$ .

Cannot be determined without knowing $P(A \mid B)$ .