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There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is
- a)1/4
- b)1/3
- c)2/3
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
There are two balls in an urn whose colours are not known (each ball c...
Probability of drawing a white ball from the urn
To find the probability of drawing a white ball from the urn, we need to consider the possible scenarios and calculate the probability for each scenario. Let's break down the problem step by step.
Step 1: Initial situation
- There are two balls in the urn, and their colors are not known.
- The possible combinations for the two balls are WW, WB, BW, and BB.
Step 2: A white ball is put into the urn
- Since a white ball is put into the urn, we can eliminate the possibility of both balls being black (BB).
- Now, the possible combinations for the two balls are WW, WB, and BW.
Step 3: Drawing a ball from the urn
- We want to find the probability of drawing a white ball from the urn.
- Let's calculate the probability for each possible combination.
Scenario 1: WW
- If both balls in the urn are white, the probability of drawing a white ball is 1.
Scenario 2: WB
- If one ball is white and the other is black, the probability of drawing a white ball is 1/2.
- This is because there is only one white ball out of two possible balls to be drawn.
Scenario 3: BW
- If one ball is black and the other is white, the probability of drawing a white ball is also 1/2.
- This is because there is only one white ball out of two possible balls to be drawn.
Step 4: Calculating the overall probability
- To find the overall probability, we need to consider the probabilities for each scenario and their likelihoods.
- The likelihood of each scenario is equal since we do not have any additional information about the colors of the balls.
- Therefore, the overall probability is the average of the probabilities for each scenario.
Overall probability = (1 + 1/2 + 1/2) / 3 = 2/3
Therefore, the probability of drawing a white ball from the urn is 2/3, which corresponds to option C.
To find the probability of drawing a white ball from the urn, we need to consider the possible scenarios and calculate the probability for each scenario. Let's break down the problem step by step.
Step 1: Initial situation
- There are two balls in the urn, and their colors are not known.
- The possible combinations for the two balls are WW, WB, BW, and BB.
Step 2: A white ball is put into the urn
- Since a white ball is put into the urn, we can eliminate the possibility of both balls being black (BB).
- Now, the possible combinations for the two balls are WW, WB, and BW.
Step 3: Drawing a ball from the urn
- We want to find the probability of drawing a white ball from the urn.
- Let's calculate the probability for each possible combination.
Scenario 1: WW
- If both balls in the urn are white, the probability of drawing a white ball is 1.
Scenario 2: WB
- If one ball is white and the other is black, the probability of drawing a white ball is 1/2.
- This is because there is only one white ball out of two possible balls to be drawn.
Scenario 3: BW
- If one ball is black and the other is white, the probability of drawing a white ball is also 1/2.
- This is because there is only one white ball out of two possible balls to be drawn.
Step 4: Calculating the overall probability
- To find the overall probability, we need to consider the probabilities for each scenario and their likelihoods.
- The likelihood of each scenario is equal since we do not have any additional information about the colors of the balls.
- Therefore, the overall probability is the average of the probabilities for each scenario.
Overall probability = (1 + 1/2 + 1/2) / 3 = 2/3
Therefore, the probability of drawing a white ball from the urn is 2/3, which corresponds to option C.
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Community Answer
There are two balls in an urn whose colours are not known (each ball c...
Let Ei (0 < i < 2) denote the event that urn contains 'i' white and '(2 – i)' black balls.
Let A denote the event that a white ball is drawn from the urn.
We have P(Ei) = 1/3 for i = 0, 1, 2
P (A|E1) = 1/3, P(A|E2) = 2/3, P(A|E3) = 1.
By the total probability rule,
P(A)= P(E1)P(A|E1) + P(E2)P(A|E2) + P(E3)P(A|E3)
Let A denote the event that a white ball is drawn from the urn.
We have P(Ei) = 1/3 for i = 0, 1, 2
P (A|E1) = 1/3, P(A|E2) = 2/3, P(A|E3) = 1.
By the total probability rule,
P(A)= P(E1)P(A|E1) + P(E2)P(A|E2) + P(E3)P(A|E3)
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There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer?
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