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Back to Apply the general Multiplication Rule — Problem 2 · Task Set 25

Exercises: Apply the General Multiplication Rule

Work through each section in order. Use the general Multiplication Rule, $P(A \text{ and } B) = P(A) \cdot P(B \mid A)$, for joint probabilities. For draws WITHOUT replacement, remember that BOTH the favorable count and the total shrink after the first draw. On a tree diagram, MULTIPLY along a path and ADD across paths. Leave fractions exact unless told otherwise.

Grade 11·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-cp-b-8
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Warm-Up: Product Rule and Conditional Probability

These problems review the prior ideas the new rule builds on.

1.

The conditional-probability formula is P(B∣A)=P(A and B)P(A)P(B \mid A) = \dfrac{P(A \text{ and } B)}{P(A)}. Suppose P(A)=0.5P(A) = 0.5 and P(A and B)=0.2P(A \text{ and } B) = 0.2. Find P(B∣A)P(B \mid A) as a decimal.