Question:
A special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. 100 III year, 150 II year, and 200 I year students have applied for the room. Each III year student’s name is placed in the lottery 3 times, each II year student’s name 2 times, and each I year student’s name 1 time. The probability that a III year student gets the room is
A special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. 100 III year, 150 II year, and 200 I year students have applied for the room. Each III year student’s name is placed in the lottery 3 times, each II year student’s name 2 times, and each I year student’s name 1 time. The probability that a III year student gets the room is
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For lottery problems with multiple entries per person, multiply the number of students by their number of entries to find total and favorable outcomes, then divide.
Updated On: Jul 18, 2026
- \(\frac{1}{8}\)
- \(\frac{2}{9}\)
- \(\frac{2}{7}\)
- \(\frac{3}{8}\)
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The Correct Option is D
Solution and Explanation
Step 1: Total entries in the lottery.
- Number of III year students = 100, each entered 3 times: \(100 \cdot 3 = 300\)
- Number of II year students = 150, each entered 2 times: \(150 \cdot 2 = 300\)
- Number of I year students = 200, each entered 1 time: \(200 \cdot 1 = 200\)
Total entries \(= 300 + 300 + 200 = 800\)
Step 2: Favorable entries for III year students.
Total favorable entries \(= 300\)
Step 3: Probability formula.
\[ P(\text{III year}) = \frac{\text{Favorable entries}}{\text{Total entries}} \]
Step 4: Apply numbers.
\[ P(\text{III year}) = \frac{300}{800} \]
Step 5: Simplify the fraction.
\[ \frac{300}{800} = \frac{3}{8} \]
Step 6: Final conclusion.
Hence, the probability that a III year student gets the room is \[ \boxed{\frac{3}{8}} \]
- Number of III year students = 100, each entered 3 times: \(100 \cdot 3 = 300\)
- Number of II year students = 150, each entered 2 times: \(150 \cdot 2 = 300\)
- Number of I year students = 200, each entered 1 time: \(200 \cdot 1 = 200\)
Total entries \(= 300 + 300 + 200 = 800\)
Step 2: Favorable entries for III year students.
Total favorable entries \(= 300\)
Step 3: Probability formula.
\[ P(\text{III year}) = \frac{\text{Favorable entries}}{\text{Total entries}} \]
Step 4: Apply numbers.
\[ P(\text{III year}) = \frac{300}{800} \]
Step 5: Simplify the fraction.
\[ \frac{300}{800} = \frac{3}{8} \]
Step 6: Final conclusion.
Hence, the probability that a III year student gets the room is \[ \boxed{\frac{3}{8}} \]
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