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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?
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Solution
Because an urn contains 5 red and 5 black balls.
(i) Suppose a red ball is drawn.
∴ Probability of drawing a red ball from a total of 10 balls = `5/10 = 1/2`
Now if two red balls are placed in the urn.
The urn contains 7 red and 5 black balls.
Probability of drawing a red ball = `7/12`
(ii) Let the black ball be drawn first.
Probability of drawing a black ball from a total of 10 balls = `5/10 = 1/2`
Two black balls are then placed in the urn.
Now the urn contains 5 red and 7 black balls.
The probability of getting a red ball = `5/12`
Probability of the second ball being red = `1/2 xx 7/12 + 1/2 xx 5/12`
= `7/24 + 5/24`
= `12/24`
= `1/2`
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