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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

35. An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

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alok kumar singh | Contributor-Level 10

4 months ago

35. Number of balls contain in win $= 5$ red

$= 5$ black

Let the red ball be drawn in the first attempt

$∴$ $P$ (drawing a red ball) $= \frac{5}{10} = \frac{1}{2}$

By question, if added two red balls to the win, then $7$ red balls and $5$ black balls contain.

$P$ (drawing a red ball) $= \frac{7}{12}$

Let a black ball be drawn at first attempt

$∴$ $P$ (drawing a black ball) $= \frac{5}{10} = \frac{1}{2}$

If two black balls are added to the win, then $7$ black balls and $5$ red balls contain.

$P$ (drawing a red ball) $= \frac{5}{12}$

Therefore, probability of drawing the second ball as of red colour is

$= (\frac{1}{2} \times \frac{7}{12}) + (\frac{1}{2} \times \frac{5}{12}) = \frac{1}{2} (\frac{7}{12} + \frac{5}{12}) = \frac{1}{2} \times \frac{12}{12} = \frac{1}{2} \times 1 = \frac{1}{2}$

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35. An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

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