Multiple choice

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. $\dfrac{26}{49}$
  2. $\dfrac{32}{49}$
  3. $\dfrac{27}{49}$
  4. $\dfrac{21}{49}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 5R, 2G. If G is drawn (prob 2/7), urn becomes 6R, 1G. If R is drawn (prob 5/7), urn becomes 4R, 3G. Prob(2nd is R) = (2/7 * 6/7) + (5/7 * 4/7) = 12/49 + 20/49 = 32/49.

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