Back to Apply the general Multiplication Rule — Problem 4 · 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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Fluency: Apply the Rule

Apply the general Multiplication Rule. For without-replacement draws, update both the favorable count and the total.

On a tree diagram for the marble bag (3 red, 2 blue, drawn without replacement), the red-then-blue path has branch probabilities $\dfrac{3}{5}$ and $\dfrac{2}{4}$ . How do you combine them to get the probability of that single path?

Multiply along the path: $\dfrac{3}{5} \cdot \dfrac{2}{4} = \dfrac{3}{10}$ .

Add along the path: $\dfrac{3}{5} + \dfrac{2}{4} = \dfrac{11}{10}$ .

Subtract: $\dfrac{3}{5} - \dfrac{2}{4} = \dfrac{1}{10}$ .

Take the larger branch probability, $\dfrac{3}{5}$ .