A probability experiment consists of two stages, in which a 6-sided die is rolled in the first stage and a marble is drawn from an urn in the second stage. If the number on the die is 1, 2, or 3, a marble is drawn from urn #1, which contains 1 green, 2 white, and 1 red marble If the number on the die is 4 or 6, a marble is drawn from urn #2, which contains 1 red, 1 blue, and 1 green marble If the number on the die is 5, a marble is drawn from urn # 3, which contains 1 green, 2 blue, and 2 white marbles a) Determine each of the following (conditional) probabilities

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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QUESTION 11
Multiplication Principle for Conditional Probabilities
A probability experiment consists of two stages, in which a 6-sided die is rolled in the first stage and a marble is drawn from an urn in the second stage.
If the number on the die is 1, 2, or 3, a marble is drawn from urn #1, which contains 1 green, 2 white, and 1 red marble
If the number on the die is 4 or 6, a marble is drawn from urn #2, which contains 1 red, 1 blue, and 1 green marble
If the number on the die is 5, a marble is drawn from urn #3, which contains 1 green, 2 blue, and 2 white marbles
a) Determine each of the following (conditional) probabilities
Pr( 'white' | 1,2, or 3)
Pr( 'white' | 5)
Pr( 'white' | 4 or 6)
Pr('green' | 4 or 6)
b) Use a tree diagram and apply the multiplication principle to find the probability corresponding to each of the branches of this tree (each of the possible outcomes for the
sample space).
Transcribed Image Text:QUESTION 11 Multiplication Principle for Conditional Probabilities A probability experiment consists of two stages, in which a 6-sided die is rolled in the first stage and a marble is drawn from an urn in the second stage. If the number on the die is 1, 2, or 3, a marble is drawn from urn #1, which contains 1 green, 2 white, and 1 red marble If the number on the die is 4 or 6, a marble is drawn from urn #2, which contains 1 red, 1 blue, and 1 green marble If the number on the die is 5, a marble is drawn from urn #3, which contains 1 green, 2 blue, and 2 white marbles a) Determine each of the following (conditional) probabilities Pr( 'white' | 1,2, or 3) Pr( 'white' | 5) Pr( 'white' | 4 or 6) Pr('green' | 4 or 6) b) Use a tree diagram and apply the multiplication principle to find the probability corresponding to each of the branches of this tree (each of the possible outcomes for the sample space).
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