the only deluxe room

[sanju09]

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?
(A) 1/8
(B) 2/9
(C) 2/7
(D) 3/8
(E) ½

[Rahul@gurome]

Each senior's name is placed 3 times and there are 100 seniors, so there are 300 senior's names placed in the lottery.
Each junior's name is placed 2 times and there are 150 juniors, so there are 300 junior's names placed in the lottery.
Each sophomore's name is placed 1 time and there are 200 sophomores, so there are 200 sophomore's names placed in the lottery.
Total number of names = 300 + 300 + 200 = 800
So, the probability that a senior's name will be chosen = 300/ 800 = 3/8

The correct answer is (D).

[kmittal82]

Since each senior's name is placed in the lottery 3 times, the total number of senior names in the lottery = 100x3 = 300
Likewise, there will be 300 (150x2) Junior's names and 200 (200x1) sophomore names.

Thus, total number of names = 300+300+200 = 800
Total number of seniors names = 300

Probability of picking a senior's name = 300/800 = 3/8, so it should be (D)