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 sophomres who applied. Each senior's junior's name , 2 times; and each sophomres who applied. Each senior's name is placed in the lottery 3 times; each junior's name ,2 times name, 2 times; and each sphomore's name , 1 time. What is the probability that a senior's name will be chosen?