. 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?

Question

Aditi Chauhan · Answer

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 · Answer

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

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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?

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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?

2 Answers

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