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Question -

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?



Answer -

Given urn contains 5red and 5 black balls.

Let in first attemptthe ball drawn is of red colour.

 P (probabilityof drawing a red ball) = 5/10 = ½

Now the two balls ofsame colour (red) are added to the urn then the urn contains 7 red and 5 blackballs.

 P (probabilityof drawing a red ball) = 7/12

Now let in firstattempt the ball drawn is of black colour.

 P (probabilityof drawing a black ball) = 5/10 = ½

Now the two balls ofsame colour (black) are added to the urn then the urn contains 5 red and 7black balls.

 P (probabilityof drawing a red ball) = 5/12

Therefore, theprobability of drawing the second ball as of red colour is:

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