JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Probability

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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:

(A) $\frac{26}{49}$
(B) $\frac{32}{49}$ ✓ Correct
(C) $\frac{27}{49}$
(D) $\frac{21}{49}$

Answer: (B)

Solution

Use total probability over the first draw. The first ball is red with probability

\frac{5}{7}

and green with probability

\frac{2}{7}

. If it was red, a green is added, leaving

4

red and

3

green, so a red second draw has chance

\frac{4}{7}

; if it was green, a red is added, leaving

6

red and

1

green, so a red second draw has chance

\frac{6}{7}

. Combining,

P (second red) = \frac{5}{7} \cdot \frac{4}{7} + \frac{2}{7} \cdot \frac{6}{7} = \frac{20}{49} + \frac{12}{49} = \frac{32}{49}

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Probability

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