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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- Ill, 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 each Year-I’s name, 1 time. What is the probability that a Year-III’s name will be chosen?
By the given information,
Total number of Year III student's name= 3*100= 300
Total number of Year II student's name= 2*150= 300
Total number of Year I student's name= 1*200= 200.
Number of favourable outcomes= year III student's name= 300
Total Sample space= total number of names= 300+300+200= 800.
Therefore, required probability= $$\ \frac{\ 300}{800}=\ \ \frac{\ 3}{8}$$- Option D
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