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  • 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.

Q.1. 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?

Answers (1)

best_answer

Black balls = 5

Red balls = 5

Total balls = 10

CASE 1  Let red ball be drawn in  first attempt.

P(drawing\, red\, ball)=\frac{5}{10}=\frac{1}{2}

Now two red balls are added in urn .

Now  red balls = 7, black balls = 5

Total balls = 12

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

CASE 2 

Let black ball be drawn in  first attempt.

P(drawing\, black\, ball)=\frac{5}{10}=\frac{1}{2}

Now two black balls are added in urn .

Now  red balls = 5, black balls = 7

Total balls = 12

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

the probability that the second ball is red =

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

= \frac{7}{24}+ \frac{5}{24}

= \frac{12}{24}=\frac{1}{2}

Posted by

seema garhwal

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