An urn contains m white and n black balls. A ball is drawn at random a

1.	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?
Answer» 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

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?

Answer»

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?

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