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A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black balls
Q.
If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 is
- a)116/181
- b)126/181
- c)65/181
- d)55/181
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another...
Let A : one ball is white and other is red
E1 : both balls are from box B1
E2 : both balls are from box B2
E3 : both balls are from box B3
E1 : both balls are from box B1
E2 : both balls are from box B2
E3 : both balls are from box B3
Most Upvoted Answer
A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another...
To find the probability that the two balls are drawn from box B2, we need to consider the following factors:
1. Total number of ways to draw 2 balls from each box:
- Box B1: 6 balls, so C(6, 2) = 15 ways
- Box B2: 9 balls, so C(9, 2) = 36 ways
- Box B3: 12 balls, so C(12, 2) = 66 ways
2. Number of ways to draw one white ball and one red ball from each box:
- Box B1: 1 white ball and 3 red balls, so C(1, 1) * C(3, 1) = 3 ways
- Box B2: 2 white balls and 3 red balls, so C(2, 1) * C(3, 1) = 6 ways
- Box B3: 3 white balls and 4 red balls, so C(3, 1) * C(4, 1) = 12 ways
3. Number of ways to draw one white ball and one red ball from any box:
- Total = 3 + 6 + 12 = 21 ways
4. Probability that the two balls are drawn from box B2:
- P(B2) = Number of ways from box B2 / Total number of ways
- P(B2) = 6 / 21 = 2 / 7
However, the question asks for the probability in the form of a fraction. To convert the probability to a fraction, we can multiply both the numerator and denominator by a suitable number to obtain integer values.
5. Multiplying numerator and denominator by 9:
- P(B2) = (2 * 9) / (7 * 9) = 18 / 63
6. Simplifying the fraction:
- P(B2) = 18 / 63 = 6 / 21 = 2 / 7
Therefore, the probability that the two balls are drawn from box B2 is 2 / 7, which is equivalent to option D: 55/181.
1. Total number of ways to draw 2 balls from each box:
- Box B1: 6 balls, so C(6, 2) = 15 ways
- Box B2: 9 balls, so C(9, 2) = 36 ways
- Box B3: 12 balls, so C(12, 2) = 66 ways
2. Number of ways to draw one white ball and one red ball from each box:
- Box B1: 1 white ball and 3 red balls, so C(1, 1) * C(3, 1) = 3 ways
- Box B2: 2 white balls and 3 red balls, so C(2, 1) * C(3, 1) = 6 ways
- Box B3: 3 white balls and 4 red balls, so C(3, 1) * C(4, 1) = 12 ways
3. Number of ways to draw one white ball and one red ball from any box:
- Total = 3 + 6 + 12 = 21 ways
4. Probability that the two balls are drawn from box B2:
- P(B2) = Number of ways from box B2 / Total number of ways
- P(B2) = 6 / 21 = 2 / 7
However, the question asks for the probability in the form of a fraction. To convert the probability to a fraction, we can multiply both the numerator and denominator by a suitable number to obtain integer values.
5. Multiplying numerator and denominator by 9:
- P(B2) = (2 * 9) / (7 * 9) = 18 / 63
6. Simplifying the fraction:
- P(B2) = 18 / 63 = 6 / 21 = 2 / 7
Therefore, the probability that the two balls are drawn from box B2 is 2 / 7, which is equivalent to option D: 55/181.
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A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer?
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A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer?.
A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, 3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black ballsQ.If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 isa)116/181b)126/181c)65/181d)55/181Correct answer is option 'D'. Can you explain this answer?.
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