Question

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?

• A. \(\frac{1}{8}\)
• B. \(\frac{2}{9}\)
• C. \(\frac{2}{7}\)
• D. \(\frac{3}{8}\)

Answer 1

The Correct Option is D

To find the probability that a Year-III student's name will be chosen, first calculate the total number of lottery entries. The approach is as follows:

1. Each Year-III student has their name placed in the lottery 3 times. There are 100 Year-III students, giving:
   \(100 \times 3 = 300\) entries.
2. Each Year-II student has their name placed in the lottery 2 times. There are 150 Year-II students, giving:
   \(150 \times 2 = 300\) entries.
3. Each Year-I student has their name placed in the lottery 1 time. There are 200 Year-I students, giving:
   \(200 \times 1 = 200\) entries.
4. Calculate the total number of entries:
   \(300 + 300 + 200 = 800\) total entries.
5. Determine the probability that a Year-III student's name is chosen. This is the ratio of Year-III entries to the total entries:
   \( \frac{300}{800} = \frac{3}{8} \).

The probability that a Year-III's name will be chosen is \( \frac{3}{8} \).