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

Answer: Option D

Solution(By Examveda Team)

Total names in the lottery,
$$\eqalign{ & = 3 \times 100 + 2 \times 150 + 200 \cr & = 800 \cr} $$
Number of Year-III's names,
$$\eqalign{ & = 3 \times 100 \cr & = 300 \cr} $$
Required probability,
$$\eqalign{ & = \frac{{300}}{{800}} \cr & = \frac{3}{8} \cr} $$