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You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?
- a)3/5
- b)2/5
- c)4/7
- d)3/7
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
You have two bags of colored marbles. Bag A contains 3 red marbles and...
Let's use conditional probability here. We want to find the probability of selecting Bag A given that a red marble was chosen.
P(A) is the probability of choosing Bag A, and P(R) is the probability of choosing a red marble.
We know that P(A) is 1/2 because we choose a bag at random, and there are two bags.
P(R|A) is the probability of choosing a red marble from Bag A, which is 3/5.
P(R|B) is the probability of choosing a red marble from Bag B, which is 4/5.
Now, we can use Bayes' theorem to find P(A|R), the probability of choosing Bag A given a red marble was picked:
P(A|R) = [P(R|A) * P(A)] / [P(R|A) * P(A) + P(R|B) * P(B)]
P(A|R) = (3/5 * 1/2) / [(3/5 * 1/2) + (4/5 * 1/2)]
P(A|R) = (3/10) / [(3/10) + (4/10)]
P(A|R) = (3/10) / (7/10)
P(A|R) = 3/7
So, the probability of selecting Bag A, given that a red marble was chosen, is 3/7, which corresponds to option D.
Most Upvoted Answer
You have two bags of colored marbles. Bag A contains 3 red marbles and...
Problem Analysis:
We are given two bags of colored marbles - Bag A and Bag B. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. We randomly choose one of the bags and then select a marble from that bag. We need to find the probability that we selected Bag A, given that we picked a red marble.
Solution:
Let's solve this problem step by step:
Step 1: Determine the probability of selecting Bag A:
Since we are choosing one of the bags at random, the probability of selecting Bag A is 1/2 (as there are two bags in total).
Step 2: Determine the probability of selecting a red marble from Bag A:
Bag A contains 3 red marbles out of a total of 5 marbles. Therefore, the probability of selecting a red marble from Bag A is 3/5.
Step 3: Determine the probability of selecting a red marble from Bag B:
Bag B contains 4 red marbles out of a total of 5 marbles. Therefore, the probability of selecting a red marble from Bag B is 4/5.
Step 4: Determine the probability of selecting a red marble:
To find the probability of selecting a red marble, we need to consider both bags. The probability of selecting a red marble can be calculated using the law of total probability, which states that the probability of an event is the sum of the probabilities of that event occurring under each possible condition.
The probability of selecting a red marble can be calculated as follows:
P(Red) = P(Red|Bag A) * P(Bag A) + P(Red|Bag B) * P(Bag B)
= (3/5) * (1/2) + (4/5) * (1/2)
= 3/10 + 4/10
= 7/10
Step 5: Determine the probability of selecting Bag A, given that we picked a red marble:
To find the probability of selecting Bag A, given that we picked a red marble, we use Bayes' theorem. Bayes' theorem states that the probability of an event occurring, given that another event has already occurred, can be calculated using the following formula:
P(A|B) = (P(B|A) * P(A)) / P(B)
In this case, we want to find P(A|Red), which represents the probability of selecting Bag A, given that we picked a red marble. Using Bayes' theorem, we can calculate this probability as follows:
P(A|Red) = (P(Red|A) * P(A)) / P(Red)
= (3/5 * 1/2) / (7/10)
= (3/10) / (7/10)
= 3/7
Therefore, the probability that Bag A was selected, given that we picked a red marble, is 3/7.
Answer:
The probability that Bag A was selected, given that we picked a red marble, is 3/7. Therefore, option D is the correct answer.
We are given two bags of colored marbles - Bag A and Bag B. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. We randomly choose one of the bags and then select a marble from that bag. We need to find the probability that we selected Bag A, given that we picked a red marble.
Solution:
Let's solve this problem step by step:
Step 1: Determine the probability of selecting Bag A:
Since we are choosing one of the bags at random, the probability of selecting Bag A is 1/2 (as there are two bags in total).
Step 2: Determine the probability of selecting a red marble from Bag A:
Bag A contains 3 red marbles out of a total of 5 marbles. Therefore, the probability of selecting a red marble from Bag A is 3/5.
Step 3: Determine the probability of selecting a red marble from Bag B:
Bag B contains 4 red marbles out of a total of 5 marbles. Therefore, the probability of selecting a red marble from Bag B is 4/5.
Step 4: Determine the probability of selecting a red marble:
To find the probability of selecting a red marble, we need to consider both bags. The probability of selecting a red marble can be calculated using the law of total probability, which states that the probability of an event is the sum of the probabilities of that event occurring under each possible condition.
The probability of selecting a red marble can be calculated as follows:
P(Red) = P(Red|Bag A) * P(Bag A) + P(Red|Bag B) * P(Bag B)
= (3/5) * (1/2) + (4/5) * (1/2)
= 3/10 + 4/10
= 7/10
Step 5: Determine the probability of selecting Bag A, given that we picked a red marble:
To find the probability of selecting Bag A, given that we picked a red marble, we use Bayes' theorem. Bayes' theorem states that the probability of an event occurring, given that another event has already occurred, can be calculated using the following formula:
P(A|B) = (P(B|A) * P(A)) / P(B)
In this case, we want to find P(A|Red), which represents the probability of selecting Bag A, given that we picked a red marble. Using Bayes' theorem, we can calculate this probability as follows:
P(A|Red) = (P(Red|A) * P(A)) / P(Red)
= (3/5 * 1/2) / (7/10)
= (3/10) / (7/10)
= 3/7
Therefore, the probability that Bag A was selected, given that we picked a red marble, is 3/7.
Answer:
The probability that Bag A was selected, given that we picked a red marble, is 3/7. Therefore, option D is the correct answer.
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You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?
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You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?.
You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You have two bags of colored marbles. Bag A contains 3 red marbles and 2 green marbles, while Bag B contains 4 red marbles and 1 green marble. You choose one of the bags at random and then select a marble from that bag. What is the probability that you selected Bag A, given that you picked a red marble?a)3/5b)2/5c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?.
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