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?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

Defence Exam > Defence Questions > Threre are 4 white and 3 black balls in a box...

Join the Discussion on the App

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?

FREE This question is part of

NDA I - Mathematics Question Paper 2014

Attempt Test

Attempt this Test

Verified Answer

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 =

View all questions of this test

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'.

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for Defence exam

Similar Defence Doubts

Directions:Each of the following sentences in this section has a blank space with four words or group of words given. Select whichever word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.The question of whether war is ever justified, and if so under what circumstances, is one which has been forcing itself ____ (1) the attention of all thoughtful men. On this question I find myself in the somewhat _ (2) position of holding that no single one of the combatants is justified in the present war, while not taking the extreme Tolstoyan view that war is under all circumstances a _ (3). Opinions on such a subject as war are the outcome of _(4) rather than of thought: given a man’s emotional temperament, his convictions, (5) on war in general, and on any particular war which may occur during his lifetime, can be __(6) with tolerable certainty. The arguments used will be mere reinforcements to convictions otherwise reached. The fundamental facts in this as in all ethical _(7) are feelings; all that thought can do is to clarify and systematize the expression of those feelings, and it ¡s such clarifying and systematizing of my own feelings that I wish to (8) in the present article. In fact, the question of right and wrongs of a particular war is generally(9) from a judicial or quasi-juridical ______ (10).

View answer

Read the following passage and answer the following questions:At this stage of civilisation, when many nations are brought in to close and vital contact for good and evil, it is important, as never before, that their gross ignorance of one another should be diminished, that they should begin to understand a little of one anothers historical experience and resulting mentality. It is the fault of the English to expect the people of other countries to react as they do, to political and international situations.Our goodwill and good intentions are often brought to nothing, because we expect other people to be like us. This would be corrected if we knew the history, not necessarily in detail but in broad outlines, of the social and political conditions which have given to each nation its present character.Q. The need for a greater understanding between nations

View answer

Read the passages carefully and choose the best answer to each question out of the four alternatives.The quest to find life outside the solar system got a big boost with the discovery of seven Earth-size extra-solar planets, or exoplanets, orbiting a dwarf star about 40 light years away. Unlike earlier discoveries of exoplanets, all seven planets could possibly have liquid water — a key to life as we know it on Earth — with three planets having the greatest chance. This is by far the largest collection of Earth-like planets in the habitable Goldilocks zone of a star — neither too close nor too far from a star, which raises the possibility of liquid water being present on the surface. Only Earth has liquid water in the solar system. Since the dwarf star is much cooler than the Sun, the dimming of light each time a planet passes or transits before the star could be easily recorded from Earth unlike in cases when planets transit a Sun-like bright star. Since the initial discovery of three planets was made using the Chile-based Transiting Planets and Planetesimals Small Telescope, the exoplanet system is called TRAPPIST-1.Q. What is the Goldilocks zone?

View answer

Read the passages carefully and choose the best answer to each question out of the four alternatives.The quest to find life outside the solar system got a big boost with the discovery of seven Earth-size extra-solar planets, or exoplanets, orbiting a dwarf star about 40 light years away. Unlike earlier discoveries of exoplanets, all seven planets could possibly have liquid water — a key to life as we know it on Earth — with three planets having the greatest chance. This is by far the largest collection of Earth-like planets in the habitable Goldilocks zone of a star — neither too close nor too far from a star, which raises the possibility of liquid water being present on the surface. Only Earth has liquid water in the solar system. Since the dwarf star is much cooler than the Sun, the dimming of light each time a planet passes or transits before the star could be easily recorded from Earth unlike in cases when planets transit a Sun-like bright star. Since the initial discovery of three planets was made using the Chile-based Transiting Planets and Planetesimals Small Telescope, the exoplanet system is called TRAPPIST-1.Q. How many planets in our solar system have liquid water?

View answer

Read the passages carefully and choose the best answer to each question out of the four alternatives.The quest to find life outside the solar system got a big boost with the discovery of seven Earth-size extra-solar planets, or exoplanets, orbiting a dwarf star about 40 light years away. Unlike earlier discoveries of exoplanets, all seven planets could possibly have liquid water — a key to life as we know it on Earth — with three planets having the greatest chance. This is by far the largest collection of Earth-like planets in the habitable Goldilocks zone of a star — neither too close nor too far from a star, which raises the possibility of liquid water being present on the surface. Only Earth has liquid water in the solar system. Since the dwarf star is much cooler than the Sun, the dimming of light each time a planet passes or transits before the star could be easily recorded from Earth unlike in cases when planets transit a Sun-like bright star. Since the initial discovery of three planets was made using the Chile-based Transiting Planets and Planetesimals Small Telescope, the exoplanet system is called TRAPPIST-1.Q. What is essential to have the possibility of life on a planet?

View answer

Share with a Friend

Answer this doubt

Question Description
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. Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.

Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice Defence tests.

Explore Courses for Defence exam