You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.You pick a random bag and take out one marble. It is a white marble.What is the probability that the remaining marble from the same bag is also white?

general knowledge math & puzzles

  1. 1/3

  2. 2/3

  3. 1

  4. 1/2

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Correct Option: B
Explanation:

To solve this question, the user needs to know the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability of selecting a white marble given that we have already selected a white marble from the same bag.

Let's use Bayes' theorem to solve the problem. Bayes' theorem states that the probability of A given B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B. In this case, we want to find the probability of selecting a white marble given that we have already selected a white marble from the same bag.

Let A be the event that the remaining marble is white, and let B be the event that we have already selected a white marble from the same bag.

So, we want to find P(A|B), which is the probability that the remaining marble is white given that we have already selected a white marble from the same bag.

From the problem statement, we know that there are three bags, and we selected one of them randomly. Thus, the probability of selecting any one of the bags is 1/3.

Now, let's consider each bag separately:

  • If we selected Bag A, then the probability of selecting a white marble is 1, since both marbles in Bag A are white. Thus, the probability that the remaining marble is white is also 1.

  • If we selected Bag B, then the probability of selecting a white marble is 0, since both marbles in Bag B are black. Thus, the probability that the remaining marble is white is 0.

  • If we selected Bag C, then the probability of selecting a white marble is 1/2, since one of the marbles in Bag C is white and the other is black. If we selected the white marble, then the remaining marble must be black. Alternatively, if we selected the black marble, then the remaining marble must be white. Thus, the probability that the remaining marble is white is 1/2.

Now, we can use the law of total probability to find the probability of selecting a white marble from any one of the bags:

P(B) = P(B|A) * P(A) + P(B|B) * P(B) + P(B|C) * P(C)

P(B) = 1 * (1/3) + 0 * (1/3) + 1/2 * (1/3)

P(B) = 1/2

Thus, the probability of selecting a white marble from any one of the bags is 1/2.

Now, we can apply Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B)

P(A|B) = 1 * (1/3) / (1/2)

P(A|B) = 2/3

Therefore, the probability that the remaining marble from the same bag is also white is 2/3.

Option B is the correct answer.

The Answer is: B. 2/3

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