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Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box is
- a)1/2
- b)6/7
- c)4/7
- d)3/7
Correct answer is option 'D'. Can you explain this answer?
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Threre are 4 white and 3 black balls in a box. In another box, there a...
Box I→4 W; 3 B
Box II→ 3 W ;4B
Probability for choosing first box =
Probability for choosing second box =
∴ Required probability =
Box II→ 3 W ;4B
Probability for choosing first box =
Probability for choosing second box =
∴ Required probability =
Most Upvoted Answer
Threre are 4 white and 3 black balls in a box. In another box, there a...
The probability that a ball was drawn from the first box, given that it is black, can be calculated using Bayes' theorem. Let's break down the problem step by step.
Step 1: Determine the probability of drawing a black ball from the first box.
In the first box, there are a total of 4 white and 3 black balls. The probability of drawing a black ball from the first box is given by:
P(Black | First Box) = Number of black balls in the first box / Total number of balls in the first box
= 3 / (3 + 4)
= 3/7
Step 2: Determine the probability of drawing a black ball from the second box.
In the second box, there are a total of 3 white and 4 black balls. The probability of drawing a black ball from the second box is given by:
P(Black | Second Box) = Number of black balls in the second box / Total number of balls in the second box
= 4 / (3 + 4)
= 4/7
Step 3: Determine the probability of rolling a number less than or equal to 3.
An unbiased dice has six sides, numbered from 1 to 6. The probability of rolling a number less than or equal to 3 is given by:
P(Roll ≤ 3) = Number of favorable outcomes / Total number of outcomes
= 3 / 6
= 1/2
Step 4: Apply Bayes' theorem to calculate the probability of drawing from the first box given that the ball drawn is black.
Using Bayes' theorem, the probability of drawing from the first box given that the ball drawn is black is given by:
P(First Box | Black) = (P(Black | First Box) * P(First Box)) / P(Black)
P(First Box | Black) = (P(Black | First Box) * P(First Box)) / (P(Black | First Box) * P(First Box) + P(Black | Second Box) * P(Second Box))
Now, let's substitute the values we calculated in the previous steps:
P(First Box | Black) = (3/7 * 1/2) / ((3/7 * 1/2) + (4/7 * 1/2))
= (3/14) / ((3/14) + (4/14))
= (3/14) / (7/14)
= 3/7
Therefore, the probability that the ball was drawn from the first box, given that it is black, is 3/7, which corresponds to option 'D'.
Step 1: Determine the probability of drawing a black ball from the first box.
In the first box, there are a total of 4 white and 3 black balls. The probability of drawing a black ball from the first box is given by:
P(Black | First Box) = Number of black balls in the first box / Total number of balls in the first box
= 3 / (3 + 4)
= 3/7
Step 2: Determine the probability of drawing a black ball from the second box.
In the second box, there are a total of 3 white and 4 black balls. The probability of drawing a black ball from the second box is given by:
P(Black | Second Box) = Number of black balls in the second box / Total number of balls in the second box
= 4 / (3 + 4)
= 4/7
Step 3: Determine the probability of rolling a number less than or equal to 3.
An unbiased dice has six sides, numbered from 1 to 6. The probability of rolling a number less than or equal to 3 is given by:
P(Roll ≤ 3) = Number of favorable outcomes / Total number of outcomes
= 3 / 6
= 1/2
Step 4: Apply Bayes' theorem to calculate the probability of drawing from the first box given that the ball drawn is black.
Using Bayes' theorem, the probability of drawing from the first box given that the ball drawn is black is given by:
P(First Box | Black) = (P(Black | First Box) * P(First Box)) / P(Black)
P(First Box | Black) = (P(Black | First Box) * P(First Box)) / (P(Black | First Box) * P(First Box) + P(Black | Second Box) * P(Second Box))
Now, let's substitute the values we calculated in the previous steps:
P(First Box | Black) = (3/7 * 1/2) / ((3/7 * 1/2) + (4/7 * 1/2))
= (3/14) / ((3/14) + (4/14))
= (3/14) / (7/14)
= 3/7
Therefore, the probability that the ball was drawn from the first box, given that it is black, is 3/7, which corresponds to option 'D'.
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Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?
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Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?.
Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer?.
Solutions for Threre are 4 white and 3 black balls in a box. In another box, there are 3 white and 4 black balls. An unbiased dice is rolled. If it shows a number less than or equal to 3, then a ball is drawn from the second box, otherwise from the first box. If the ball drawn is black then the possibility that the ball was drawn from the first box isa)1/2b)6/7c)4/7d)3/7Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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