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(a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?

(a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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10. Box A has 3 green marbles and 1 red marble, box B has 4 green marbles and 2 red marbles, and box C has 5 green marbles and 3 red marbles. Peter rolls a die first. If the die comes up 1, then he will randomly choose a marble from box A; if the die comes up 2 or 3, he will randomly choose a marble from box B; if the die comes up 4, 5 or 6, he will randomly choose a marble from box C. (a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?
Transcribed Image Text:10. Box A has 3 green marbles and 1 red marble, box B has 4 green marbles and 2 red marbles, and box C has 5 green marbles and 3 red marbles. Peter rolls a die first. If the die comes up 1, then he will randomly choose a marble from box A; if the die comes up 2 or 3, he will randomly choose a marble from box B; if the die comes up 4, 5 or 6, he will randomly choose a marble from box C. (a) What is the probability that Peter gets a red marble? (b) If it's known that Peter gets a red marble, what is the probability that the marble is chosen from box A? (c) If it's known that Peter gets a green marble, what is the probability that the marble is chosen from box C?
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