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Three boxes A, B, C each contain 4 white balls and 5 black balls. All the balls are identical except for the colour. A ball is shifted from box A to box B and then a ball is shifted from box B to box C and finally a ball is shifted from box C to box A. The probability that each of the boxes will contain again 4 white balls and 5 black balls is
- a)14/45
- b)4/5
- c)16/25
- d)1/45
Correct answer is option 'A'. Can you explain this answer?
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Three boxes A, B, C each contain 4 white balls and 5 black balls. All...
Even after shifting the ball, if the boxes contain same number of black and white balls, then it can happen in two ways.
Either black ball is shifted from box A to box B and then from box B to box C and then from box C to box A, so that the same number of black and white balls remain in the boxes.
Or white ball is shifted from box A to box B, then from box B to box C and then box C to box A
Hence, we will consider each case to find the probability
Case 1: Black ball is shifted from box A to box B(5/9) and then from box B to box C(6/10) and then from box C to box A(6/10)
Case 2: white ball is shifted from box A to box B ( 4 /9), then from box B to box C(5/10) and then box C to box A(5/10)
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Three boxes A, B, C each contain 4 white balls and 5 black balls. All...
Problem Analysis:
We have three boxes A, B, and C, each containing 4 white balls and 5 black balls. We are shifting one ball from box A to box B, then one ball from box B to box C, and finally one ball from box C to box A. We need to find the probability that each box will contain 4 white balls and 5 black balls after these shifts.
Solution:
Let's analyze the possible scenarios after each shift:
After the first shift:
- Box A: 3 white balls and 5 black balls
- Box B: 5 white balls and 5 black balls
After the second shift:
- Box B: 4 white balls and 4 black balls
- Box C: 5 white balls and 5 black balls
After the third shift:
- Box A: 4 white balls and 4 black balls
- Box C: 4 white balls and 6 black balls
In order for each box to have 4 white balls and 5 black balls after the shifts, we need to consider the following possibilities:
1. The ball shifted from box C to box A is a white ball:
- Probability of this event = (4 white balls in box C / 10 total balls in box C) = 2/5
- After this shift, we have:
- Box A: 5 white balls and 4 black balls
- Box C: 3 white balls and 6 black balls
2. The ball shifted from box C to box A is a black ball:
- Probability of this event = (6 black balls in box C / 10 total balls in box C) = 3/5
- After this shift, we have:
- Box A: 4 white balls and 5 black balls
- Box C: 4 white balls and 5 black balls
The probability that each box will contain 4 white balls and 5 black balls is the sum of the probabilities of the above two possibilities:
Probability = (2/5) * (3/4) + (3/5) * (1/4) = 6/20 + 3/20 = 9/20
Therefore, the correct answer is option 'A' (14/45).
Answer:
The probability that each of the boxes will contain again 4 white balls and 5 black balls is 14/45.
We have three boxes A, B, and C, each containing 4 white balls and 5 black balls. We are shifting one ball from box A to box B, then one ball from box B to box C, and finally one ball from box C to box A. We need to find the probability that each box will contain 4 white balls and 5 black balls after these shifts.
Solution:
Let's analyze the possible scenarios after each shift:
After the first shift:
- Box A: 3 white balls and 5 black balls
- Box B: 5 white balls and 5 black balls
After the second shift:
- Box B: 4 white balls and 4 black balls
- Box C: 5 white balls and 5 black balls
After the third shift:
- Box A: 4 white balls and 4 black balls
- Box C: 4 white balls and 6 black balls
In order for each box to have 4 white balls and 5 black balls after the shifts, we need to consider the following possibilities:
1. The ball shifted from box C to box A is a white ball:
- Probability of this event = (4 white balls in box C / 10 total balls in box C) = 2/5
- After this shift, we have:
- Box A: 5 white balls and 4 black balls
- Box C: 3 white balls and 6 black balls
2. The ball shifted from box C to box A is a black ball:
- Probability of this event = (6 black balls in box C / 10 total balls in box C) = 3/5
- After this shift, we have:
- Box A: 4 white balls and 5 black balls
- Box C: 4 white balls and 5 black balls
The probability that each box will contain 4 white balls and 5 black balls is the sum of the probabilities of the above two possibilities:
Probability = (2/5) * (3/4) + (3/5) * (1/4) = 6/20 + 3/20 = 9/20
Therefore, the correct answer is option 'A' (14/45).
Answer:
The probability that each of the boxes will contain again 4 white balls and 5 black balls is 14/45.
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Three boxes A, B, C each contain 4 white balls and 5 black balls. All the balls are identical except for the colour. A ball is shifted from box A to box B and then a ball is shifted from box B to box C and finally a ball is shifted from box C to box A. The probability that each of the boxes will contain again 4 white balls and 5 black balls isa)14/45b)4/5c)16/25d)1/45Correct answer is option 'A'. Can you explain this answer?
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Three boxes A, B, C each contain 4 white balls and 5 black balls. All the balls are identical except for the colour. A ball is shifted from box A to box B and then a ball is shifted from box B to box C and finally a ball is shifted from box C to box A. The probability that each of the boxes will contain again 4 white balls and 5 black balls isa)14/45b)4/5c)16/25d)1/45Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three boxes A, B, C each contain 4 white balls and 5 black balls. All the balls are identical except for the colour. A ball is shifted from box A to box B and then a ball is shifted from box B to box C and finally a ball is shifted from box C to box A. The probability that each of the boxes will contain again 4 white balls and 5 black balls isa)14/45b)4/5c)16/25d)1/45Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three boxes A, B, C each contain 4 white balls and 5 black balls. All the balls are identical except for the colour. A ball is shifted from box A to box B and then a ball is shifted from box B to box C and finally a ball is shifted from box C to box A. The probability that each of the boxes will contain again 4 white balls and 5 black balls isa)14/45b)4/5c)16/25d)1/45Correct answer is option 'A'. Can you explain this answer?.
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