JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Probability

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A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

(A) $\frac{1}{4}$
(B) $\frac{9}{50}$
(C) $\frac{1}{5}$ ✓ Correct
(D) $\frac{11}{50}$

Answer: (C)

Solution

By total probability over the die outcome

k

, the chance the

k

drawn balls are all white is

\frac{1}{6} \cdot \frac{( k 6 )}{( k 10 )}

. Summing over

k = 1, \dots, 6

P = \frac{1}{6} (\frac{6}{10} + \frac{15}{45} + \frac{20}{120} + \frac{15}{210} + \frac{6}{252} + \frac{1}{210})

. Taking each term over

210

gives

\frac{126 + 70 + 35 + 15 + 5 + 1}{210} = \frac{252}{210}

. Therefore

P = \frac{1}{6} \cdot \frac{252}{210} = \frac{1}{5}

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Single correct option

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