JEE Main · 2018 · 08 Apr 2018 · Offline · Probability

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A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

(A) $\frac{3}{4}$
(B) $\frac{3}{10}$
(C) $\frac{2}{5}$ ✓ Correct
(D) $\frac{1}{5}$

Answer: (C)

Solution

Condition on the first draw. The first ball is red with probability

\frac{4}{10} = \frac{2}{5}

, after which the bag holds

7

red among

13

, so the second is red with probability

\frac{7}{13}

. The first is black with probability

\frac{3}{5}

, after which the bag holds

4

red among

13

, giving

\frac{4}{13}

. The total probability is

\frac{2}{5} \cdot \frac{7}{13} + \frac{3}{5} \cdot \frac{4}{13} = \frac{14 + 12}{65} = \frac{26}{65} = \frac{2}{5}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option

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JEE Main · 2018 · 08 Apr 2018 · Offline · Probability

Solution

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