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Question

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is : 
  1. 2749
  2. 2149
  3. 2649
  4. 3249


Solution

The correct option is D 3249
Let E1 : Event of drawing green and adding red ball. 
E2 : Event of drawing red and adding green ball. 
G : Event of drawing a red ball in the second draw 
P(G)=P(E1)P(G|E1)+P(E2)P(G|E2)
P(G)=27×67+57×47
P(G)=3249

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