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A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectively
- a)6/321 and 3/926
- b)1/20 and 1/30
- c)35/144 and 35/108
- d)7/968 and 5/264
Correct answer is option 'D'. Can you explain this answer?
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A box contains 5 white and 7 black balls. Two successive drawn of 3 ba...
Given:
- A box contains 5 white and 7 black balls.
- Two successive draws of 3 balls are made.
We need to find the probability that the first draw would produce white balls and the second draw would produce black balls respectively for both cases - with replacement and without replacement.
With Replacement:
In this case, after each draw, the ball is replaced before the next draw. Thus, the probability of getting a white ball remains unchanged for each draw.
Probability of getting a white ball in one draw = 5/12
Probability of getting a black ball in one draw = 7/12
Probability of getting 3 white balls in two draws = (5/12)^3 = 125/1728
Probability of getting 2 white balls and 1 black ball in two draws = 3(5/12)^2(7/12) = 175/1728
Probability of getting 1 white ball and 2 black balls in two draws = 3(5/12)(7/12)^2 = 245/1728
Probability of getting 3 black balls in two draws = (7/12)^3 = 343/1728
Probability of getting a white ball followed by two black balls = (125/1728) * (343/1728) = 7/968
Without Replacement:
In this case, after each draw, the ball is not replaced before the next draw. Thus, the probability of getting a white ball changes for each draw.
Probability of getting a white ball in the first draw = 5/12
Probability of getting a black ball in the first draw = 7/12
Probability of getting a white ball in the second draw, given that the first draw was a white ball = 4/11
Probability of getting a black ball in the third draw, given that the first two draws were white balls = 6/10 = 3/5
Probability of getting a white ball followed by two black balls = (5/12) * (7/11) * (3/5) = 5/264
Thus, the correct option is D) 7/968 and 5/264.
- A box contains 5 white and 7 black balls.
- Two successive draws of 3 balls are made.
We need to find the probability that the first draw would produce white balls and the second draw would produce black balls respectively for both cases - with replacement and without replacement.
With Replacement:
In this case, after each draw, the ball is replaced before the next draw. Thus, the probability of getting a white ball remains unchanged for each draw.
Probability of getting a white ball in one draw = 5/12
Probability of getting a black ball in one draw = 7/12
Probability of getting 3 white balls in two draws = (5/12)^3 = 125/1728
Probability of getting 2 white balls and 1 black ball in two draws = 3(5/12)^2(7/12) = 175/1728
Probability of getting 1 white ball and 2 black balls in two draws = 3(5/12)(7/12)^2 = 245/1728
Probability of getting 3 black balls in two draws = (7/12)^3 = 343/1728
Probability of getting a white ball followed by two black balls = (125/1728) * (343/1728) = 7/968
Without Replacement:
In this case, after each draw, the ball is not replaced before the next draw. Thus, the probability of getting a white ball changes for each draw.
Probability of getting a white ball in the first draw = 5/12
Probability of getting a black ball in the first draw = 7/12
Probability of getting a white ball in the second draw, given that the first draw was a white ball = 4/11
Probability of getting a black ball in the third draw, given that the first two draws were white balls = 6/10 = 3/5
Probability of getting a white ball followed by two black balls = (5/12) * (7/11) * (3/5) = 5/264
Thus, the correct option is D) 7/968 and 5/264.
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A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectivelya)6/321 and 3/926b)1/20 and 1/30c)35/144 and 35/108d)7/968 and 5/264Correct answer is option 'D'. Can you explain this answer?
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A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectivelya)6/321 and 3/926b)1/20 and 1/30c)35/144 and 35/108d)7/968 and 5/264Correct answer is option 'D'. Can you explain this answer? 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 A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectivelya)6/321 and 3/926b)1/20 and 1/30c)35/144 and 35/108d)7/968 and 5/264Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectivelya)6/321 and 3/926b)1/20 and 1/30c)35/144 and 35/108d)7/968 and 5/264Correct answer is option 'D'. Can you explain this answer?.
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