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What is the probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it was found to be white
- a)1/20
- b)1/10
- c)1/2
- d)1/4
Correct answer is option 'C'. Can you explain this answer?
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What is the probability that an urn containing 5 balls contains only w...
This conditional probability is equal
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What is the probability that an urn containing 5 balls contains only w...
To solve this problem, we can use the concept of conditional probability. Let's break down the problem step by step.
Step 1: Determine the total number of possible outcomes
The urn contains 5 balls, and each ball can either be white or not white (let's assume there are no other colors). Since there are two possibilities for each ball, the total number of possible outcomes is 2^5 = 32.
Step 2: Determine the number of favorable outcomes
Since the first two balls drawn are white, we know that at least two of the five balls are white. We need to find the number of ways to arrange the remaining three balls (which can be either white or not white) in the urn.
To do this, we can use combinations. We have 3 slots to fill with 2 possibilities (white or not white). The number of ways to arrange them is given by the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of slots and k is the number of slots to be filled.
In this case, we have 3 slots and 2 possibilities (white or not white), so the number of ways to arrange them is C(3, 2) = 3! / (2!(3-2)!) = 3.
Therefore, the number of favorable outcomes is 3.
Step 3: Calculate the probability
The probability is given by the formula: Probability = Number of favorable outcomes / Total number of possible outcomes.
In this case, the probability is: Probability = 3 / 32 = 1/2.
Answer: The probability that the urn contains only white balls, given that the first two balls drawn were white, is 1/2 (option C).
Step 1: Determine the total number of possible outcomes
The urn contains 5 balls, and each ball can either be white or not white (let's assume there are no other colors). Since there are two possibilities for each ball, the total number of possible outcomes is 2^5 = 32.
Step 2: Determine the number of favorable outcomes
Since the first two balls drawn are white, we know that at least two of the five balls are white. We need to find the number of ways to arrange the remaining three balls (which can be either white or not white) in the urn.
To do this, we can use combinations. We have 3 slots to fill with 2 possibilities (white or not white). The number of ways to arrange them is given by the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of slots and k is the number of slots to be filled.
In this case, we have 3 slots and 2 possibilities (white or not white), so the number of ways to arrange them is C(3, 2) = 3! / (2!(3-2)!) = 3.
Therefore, the number of favorable outcomes is 3.
Step 3: Calculate the probability
The probability is given by the formula: Probability = Number of favorable outcomes / Total number of possible outcomes.
In this case, the probability is: Probability = 3 / 32 = 1/2.
Answer: The probability that the urn contains only white balls, given that the first two balls drawn were white, is 1/2 (option C).
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What is the probability that an urn containing 5 balls contains only white balls if the first two balls drawn from it was found to be whitea)1/20b)1/10c)1/2d)1/4Correct answer is option 'C'. Can you explain this answer?
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