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A Bag contains 5 red and 2 green balls. One ball is drawn at random. If the drawn ball is red, then a green ball is added in the bag. If the drawn ball is green, then a red ball is added to the urn find the probability that this ball is red.

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Let, A: Event of drawing a red ball and placing a green ball in the bag.

        B: Event of drawing a green ball and placing a red ball in the bag.

        c: Event of drawing a red ball in the second draw. 

 

P(C) = P(A)\cdot P\left(\frac{C}{A} \right ) + P(B)\cdot P\left(\frac{C}{B} \right ) \\ = \frac{5}{7}\times \frac{4}{7} + \frac{2}{7}\times \frac{6}{7} \\ = \frac{32}{49}

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Pankaj Sanodiya

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