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. An urn contains m white and n black balls. A ball is drawn at random and is put back into urn along with k additional balls of the same color as that of the ball drawn. A ball is again drawn at random. What is the probability that the ball drawn now is white?

. An urn contains m white and n black balls. A ball is drawn at random and is put back into urn along with k additional balls of the same color as that of the ball drawn. A ball is again drawn at random. What is the probability that the ball drawn now is white?

Grade:11

2 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Hello Student,
Please find the answer to your question
Let W1 (B1) be the event that a white (a black) ball is drawn in the first draw and let W be the event that a white ball is drawn in the second draw. Then
P (W) = P (B1). P (W| B1) + P (W1). P (W| W1)
= n/m + n. m/m + n + k + m/m + n. m + k/m + n + k
= m(n + m + k)/(m + n) (m + n + k) = m/m + n

Thanks
Aditi Chauhan
askIITians Faculty
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

Let W1 (B1) be the event that a white (a black) ball is drawn in the first draw and let W be the event that a white ball is drawn in the second draw. Then
P (W) = P (B1). P (W| B1) + P (W1). P (W| W1)
= n/m + n. m/m + n + k + m/m + n. m + k/m + n + k
= m(n + m + k)/(m + n) (m + n + k) = m/m + n

Thanks and Regards

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