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RD Sharma - Volume 2

Exercise 31.1

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Exercise 31.2

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Exercise 31.3

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Exercise 31.4

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Exercise 31.5

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Exercise 31.6

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Exercise 31.7

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Very short answer

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Q. 45.0( 2 Votes )

A bag contains 3 white and 2 black balls, and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.

Class 12th RD Sharma - Volume 2 31. Probability

Answer :

Given:

The bag I contains 3 white and 2 black balls.

Bag II contains 2 white and 4 black balls.

A bag is chosen, and a ball is drawn from it.

There are two mutually exclusive ways to draw a white ball from one of the two bags –

a. The bag I is selected, and then, a white ball is drawn from the bag I

b. Bag II is selected, and then, a white ball is drawn from bag II

Let E₁ be the event that bag I is selected and E₂ be the event that bag II is selected.

Since there are only two bags and each bag has an equal probability of being selected, we have

Let E₃ denote the event that a white ball is drawn.

Hence, we have

We also have

Using the theorem of total probability, we get

P(E₃) = P(E₁)P(E₃|E₁) + P(E₂)P(E₃|E₂)

Thus, the probability of the drawn ball being white is.

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PREVIOUSOne bag contains 4 yellow and 5 red balls. Another bag contains 6 yellow and 3 red balls. A ball is transferred from the first bag to the second bag, and then a ball is drawn from the second bag. Find the probability that ball drawn is yellow.NEXTThe contents of three bags I, II and III are as follows:Bag I: 1 white, 2 black and 3 red ballsBag II: 2 white, 1 black and 1 red ballBag III: 4 white, 5 black and 3 red ballsA bag is chosen at random and two balls are drawn. What is the probability that the balls drawn are white and red?

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