A special lottery is to be held to select a student who will live in the only deluxe room available in a…
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 student's name is placed in the lottery 3 times, each II year student's name 2 times and I year student's name 1 time. The probability that a III year student gets the room is
$\frac{1}{8}$
$\frac{2}{9}$
$\frac{2}{7}$
$\frac{3}{8}$
Solution
Number of slip for III year student $=3 \times 100=300$
Number of slip for II year student $=2 \times 150=300$
Number of slip for I year student $=1 \times 200=200$
Required probability $=\frac{300}{300+300+200}=\frac{300}{800}=\frac{3}{8}$