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A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the - Mathematics

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Question

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

Sum

Solution

Let the events of choosing the first and second bag be E1 and E2 respectively, then

P(E1) = P(E2) = `1/2`

Let E be the event of drawing red balls, then

P(E|E1) = `4/8 = 1/2`, P(E|E2) = `2/8 = 1/4`

Now, what is the probability of drawing a ball from the first bag when it is known that it is red in colour.

= P(E1|E)

By Bayes' theorem P(E1|E) = `(P(E_1) xx P(E|E_1))/(P(E_1) xx P(E|E_1) + P(E_2) xx P(E|E_2))`

= `(1/2 xx 1/2)/(1/2 xx 1/2 + 1/2 xx 1/4)`

= `(1/4)/(1/4 + 1/8)`

= `1/4 xx 8/3`

= `2/3`

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Chapter 13: Probability - Exercise 13.3 [Page 556]

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NCERT Mathematics [English] Class 12
Chapter 13 Probability
Exercise 13.3 | Q 2 | Page 556

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