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A special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. 100 III year, 150 II year and 200 I year students have applied for the room. Each III year students name is placed in the lottery 3 times, each II year students name 2 times and I year students name 1 time. The probability that a III year students gets the room is

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$\frac{1}{8}$

$\frac{9}{10}$

$\frac{2}{7}$

$\frac{3}{8}$

answer is D.

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Detailed Solution

Requiredprobability $= \frac{\frac{2}{9} \times \frac{1}{2}}{\frac{4}{9} \times \frac{1}{6} + \frac{1}{3} \times \frac{1}{3} + \frac{2}{9} \times \frac{1}{2}} = \frac{3}{8}$

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