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1. A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?

A. $\frac{1}{8}$

B. $\frac{2}{9}$

C. $\frac{2}{7}$

D. $\frac{3}{8}$

Solution:

Total names in the lottery,

\begin{aligned} = 3 \times 100 + 2 \times 150 + 200 \\ = 800 \end{aligned}

Number of Year-III's names,

\begin{aligned} = 3 \times 100 \\ = 300 \end{aligned}

Required probability,

\begin{aligned} = \frac{300}{800} \\ = \frac{3}{8} \end{aligned}

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