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In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:
- a)11/17
- b)12/17
- c)13/18
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a bag there are 12 black and 6 white balls. Two balls are chosen at...
11/17 (if the first one is black, there will be 11 black balls left out of 17)
Most Upvoted Answer
In a bag there are 12 black and 6 white balls. Two balls are chosen at...
Probability of choosing a black ball as the first ball:
There are 12 black balls out of a total of 18 balls in the bag. Therefore, the probability of choosing a black ball as the first ball is given by:
P(Black) = 12/18 = 2/3
Probability of choosing a black ball as the second ball:
After the first ball is chosen and found to be black, there are now 11 black balls left out of a total of 17 balls in the bag. Therefore, the probability of choosing a black ball as the second ball, given that the first ball is black, is given by:
P(Black|Black) = 11/17
Explanation:
When the first ball is chosen and found to be black, it reduces the total number of balls in the bag to 17. Out of these 17 balls, there are still 11 black balls remaining. Therefore, the probability of choosing a black ball as the second ball, given that the first ball is black, is 11/17.
The reason why the answer is not 12/17 is because the first black ball that was chosen is not put back into the bag. Therefore, the total number of balls in the bag is reduced by 1, and the total number of black balls is also reduced by 1.
Since the two events (choosing the first ball and choosing the second ball) are dependent, we need to use conditional probability to calculate the probability of the second ball being black given that the first ball is black.
Therefore, the correct answer is option A) 11/17, which represents the probability of the second ball being black given that the first ball is black.
There are 12 black balls out of a total of 18 balls in the bag. Therefore, the probability of choosing a black ball as the first ball is given by:
P(Black) = 12/18 = 2/3
Probability of choosing a black ball as the second ball:
After the first ball is chosen and found to be black, there are now 11 black balls left out of a total of 17 balls in the bag. Therefore, the probability of choosing a black ball as the second ball, given that the first ball is black, is given by:
P(Black|Black) = 11/17
Explanation:
When the first ball is chosen and found to be black, it reduces the total number of balls in the bag to 17. Out of these 17 balls, there are still 11 black balls remaining. Therefore, the probability of choosing a black ball as the second ball, given that the first ball is black, is 11/17.
The reason why the answer is not 12/17 is because the first black ball that was chosen is not put back into the bag. Therefore, the total number of balls in the bag is reduced by 1, and the total number of black balls is also reduced by 1.
Since the two events (choosing the first ball and choosing the second ball) are dependent, we need to use conditional probability to calculate the probability of the second ball being black given that the first ball is black.
Therefore, the correct answer is option A) 11/17, which represents the probability of the second ball being black given that the first ball is black.
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In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a bag there are 12 black and 6 white balls. Two balls are chosen at random and the first one is found to be black. The probability that the second one is also black is:a)11/17b)12/17c)13/18d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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