Question

# A bag contains three red marbles, one yellow marble, and six green marbles. Two marbles are...

A bag contains three red marbles, one yellow marble, and six green marbles. Two marbles are drawn from the bag with replacement. One marble is drawn, the color is recorded, and the marble is returned to the bag. A second marble is drawn from the bag and the color is recorded.

a. What is the probability that both marbles are yellow?

b. What is the probability that both marbles are red?

c. What is the probability of drawing one green and one red marble?

d. Given that the first marble drawn is green, what is the probability that the second marble drawn is yellow?

e. What is the probability that neither marble is green?

Solution: We are given that there are three red marbles, one yellow marble, six green marbles. Therefore, there are 10 marbles in total in a bag.

a. What is the probability that both marbles are yellow?

Answer: The probability that both marbles are yellow is:

b. What is the probability that both marbles are red?

Answer: The probability that both marbles are red is:

c. What is the probability of drawing one green and one red marble?

Answer: The probability of drawing one green and one red marble is:

d. Given that the first marble drawn is green, what is the probability that the second marble drawn is yellow?

Answer: The probability that the second marble drawn is yellow given that the first marble drawn is green is:

e. What is the probability that neither marble is green?

Answer: The probability that neither marble is green is:

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The text passage contains a series of probability questions related to drawing marbles from a bag with replacement, and it provides a solution structure with placeholders for the answers.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Question

# A bag contains three red marbles, one yellow marble, and six green marbles. Two marbles are...

A bag contains three red marbles, one yellow marble, and six green marbles. Two marbles are drawn from the bag with replacement. One marble is drawn, the color is recorded, and the marble is returned to the bag. A second marble is drawn from the bag and the color is recorded.

a. What is the probability that both marbles are yellow?

b. What is the probability that both marbles are red?

c. What is the probability of drawing one green and one red marble?

d. Given that the first marble drawn is green, what is the probability that the second marble drawn is yellow?

e. What is the probability that neither marble is green?

Solution: We are given that there are three red marbles, one yellow marble, six green marbles. Therefore, there are 10 marbles in total in a bag.

a. What is the probability that both marbles are yellow?

Answer: The probability that both marbles are yellow is:

b. What is the probability that both marbles are red?

Answer: The probability that both marbles are red is:

c. What is the probability of drawing one green and one red marble?

Answer: The probability of drawing one green and one red marble is:

d. Given that the first marble drawn is green, what is the probability that the second marble drawn is yellow?

Answer: The probability that the second marble drawn is yellow given that the first marble drawn is green is:

e. What is the probability that neither marble is green?

Answer: The probability that neither marble is green is:

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Coins can be redeemed for fabulous gifts.
user
The text passage contains a series of probability questions related to drawing marbles from a bag with replacement, and it provides a solution structure with placeholders for the answers.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS