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There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red?
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There are two urns containing 5 red and 6 white balls and 3 red and 7 ...
Solution:
Given,
- Urn 1 contains 5 red and 6 white balls
- Urn 2 contains 3 red and 7 white balls
Let's calculate the probability of drawing two red balls from Urn 1:
- Probability of drawing one red ball in the first draw = 5/11
- Probability of drawing another red ball in the second draw without replacement = 4/10
- Probability of drawing two red balls from Urn 1 = (5/11) * (4/10) = 2/11
Now, let's calculate the probability of transferring two balls from Urn 1 to Urn 2 without replacement:
- Probability of transferring one red ball from Urn 1 to Urn 2 = (5/11) * (7/10) = 35/110
- Probability of transferring one white ball from Urn 1 to Urn 2 = (6/11) * (7/10) = 42/110
- Probability of transferring two red balls from Urn 1 to Urn 2 = (5/11) * (4/10) * (3/9) * (7/8) = 105/792
- Probability of transferring one red and one white ball from Urn 1 to Urn 2 = (5/11) * (6/10) * (3/9) * (7/8) + (6/11) * (5/10) * (4/9) * (7/8) = 210/792
Finally, let's calculate the probability of drawing two red balls from Urn 2 after two balls have been transferred from Urn 1:
- Probability of drawing one red ball in the first draw = 3/12
- Probability of drawing another red ball in the second draw without replacement = 2/11
- Probability of drawing two red balls from Urn 2 = (3/12) * (2/11) = 1/22
Therefore, the probability that both balls drawn are red after two balls are transferred from Urn 1 to Urn 2 and then two balls are drawn from Urn 2 is:
- Probability of transferring two red balls from Urn 1 to Urn 2 * Probability of drawing two red balls from Urn 2 = (105/792) * (1/22) = 5/1584
Hence, the probability that both balls drawn are red is 5/1584.
Given,
- Urn 1 contains 5 red and 6 white balls
- Urn 2 contains 3 red and 7 white balls
Let's calculate the probability of drawing two red balls from Urn 1:
- Probability of drawing one red ball in the first draw = 5/11
- Probability of drawing another red ball in the second draw without replacement = 4/10
- Probability of drawing two red balls from Urn 1 = (5/11) * (4/10) = 2/11
Now, let's calculate the probability of transferring two balls from Urn 1 to Urn 2 without replacement:
- Probability of transferring one red ball from Urn 1 to Urn 2 = (5/11) * (7/10) = 35/110
- Probability of transferring one white ball from Urn 1 to Urn 2 = (6/11) * (7/10) = 42/110
- Probability of transferring two red balls from Urn 1 to Urn 2 = (5/11) * (4/10) * (3/9) * (7/8) = 105/792
- Probability of transferring one red and one white ball from Urn 1 to Urn 2 = (5/11) * (6/10) * (3/9) * (7/8) + (6/11) * (5/10) * (4/9) * (7/8) = 210/792
Finally, let's calculate the probability of drawing two red balls from Urn 2 after two balls have been transferred from Urn 1:
- Probability of drawing one red ball in the first draw = 3/12
- Probability of drawing another red ball in the second draw without replacement = 2/11
- Probability of drawing two red balls from Urn 2 = (3/12) * (2/11) = 1/22
Therefore, the probability that both balls drawn are red after two balls are transferred from Urn 1 to Urn 2 and then two balls are drawn from Urn 2 is:
- Probability of transferring two red balls from Urn 1 to Urn 2 * Probability of drawing two red balls from Urn 2 = (105/792) * (1/22) = 5/1584
Hence, the probability that both balls drawn are red is 5/1584.
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There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red?
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There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red?.
There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red?.
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