K12worX
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
Work through problems with immediate feedback
A

Fluency: Apply the Rule

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

1.

Two cards are drawn from a standard 52-card deck without replacement. Find P(both kings)P(\text{both kings}) by filling each blank. First king: P=452P = \dfrac{4}{52}. After a king is removed,   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   kings remain among   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cards, so the second factor is 3000000\dfrac{3}{\text{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}}. The joint probability, in lowest terms, is 1000000\dfrac{1}{\text{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}}.

kings remaining:
cards remaining:
second-draw denominator:
denominator of P(both kings) in lowest terms: