Problem preview

S-CP.5 Core M2-067-R10-V03

Explain conditional probability and independence in everyday language and situations.

Distinguish a conditional probability from its reverse

Problem

Use the deck table to compare \(P(\text{face}|\text{king})=4/4\) with \(P(\text{king}|\text{face})=4/12\). Explain the change in denominator when the condition reverses.

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P(face|king) = 4/12 = 1/3; P(king|face) = 4/4 = 1, so they are not equal.

Both probabilities equal 4/4 = 1 because every king is a face card.

P(face|king) = 4/4 = 1; P(king|face) = 4/12 = 1/3, so they are not equal.

Both probabilities equal 4/52 = 1/13 because the deck has 52 cards.

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Curriculum context

Course: Math II
Standard: S-CP.5
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Explain conditional probability and independence in everyday language and situations.
Problem type: Distinguish a conditional probability from its reverse