JEE PYQ: Probability Question 42
Question 42 - 2019 (09 Jan Shift 2)
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) $\frac{21}{49}$
(2) $\frac{27}{49}$
(3) $\frac{26}{49}$
(4) $\frac{32}{49}$
Show Answer
Answer: (4)
Solution
$P(R_2) = P(G_1)P(R_2|G_1) + P(R_1)P(R_2|R_1) = \frac{2}{7} \times \frac{6}{7} + \frac{5}{7} \times \frac{4}{7} = \frac{12 + 20}{49} = \frac{32}{49}$.
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