Question

A special lottery is to be held to select one 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 student's name is placed in the lottery drum 3 times, each Year-II student's name 2 times, and each Year-I student's name 1 time. What is the probability that a Year-III student's name will be drawn?

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

Hint:

Total slips = (students x entries per student) added across all three groups; probability for Year-III = its slip count divided by the total.

Answer 1

The Correct Option is D

Step 1: Count the total number of slips contributed by each group.
Year-III: 100 students, each entered 3 times, giving \(100 \times 3 = 300\) slips.
Year-II: 150 students, each entered 2 times, giving \(150 \times 2 = 300\) slips.
Year-I: 200 students, each entered 1 time, giving \(200 \times 1 = 200\) slips.

Step 2: Find the total number of slips in the drum.
\[ 300 + 300 + 200 = 800 \]

Step 3: Identify the favourable outcomes.
A Year-III student's name is drawn if any one of the 300 Year-III slips is picked, since each slip represents an equally likely draw.

Step 4: Compute the probability.
\[ P(\text{Year-III}) = \frac{300}{800} = \frac{3}{8} \]

Step 5: Rule out the other options.
\(\frac{1}{8}\) and \(\frac{2}{9}\) and \(\frac{2}{7}\) do not equal \(\frac{300}{800}\) in lowest terms; only \(\frac{3}{8}\) matches the actual slip count.

Final Answer:
The probability that a Year-III student's name is chosen is \(\frac{3}{8}\).
\[ \boxed{\frac{3}{8}} \]