Question

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

Answer 1

Let W1 = ball drawn in the first draw is white. B1 = ball drawn in the first draw in black. W2 = ball drawn in the second draw in white. Then, P(W2)=P(W1)P(W2/W1)+P(B1)P(W2/B1) =( m m+n )( m+k m+n+k )+( n m+n )( m m+n+k ) = m(m+k)+mn (m+n)(m+n+k) = m(m+n+k) (m+n)(m+n+k) = m m+n