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Probability and Statistics

GATE CSE 2014 Set 2 · Q2

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Each of the nine words in the sentence "The quick brown fox jumps over the lazy dog" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The *expected length* of the word drawn is _________. (The answer should be rounded to one decimal place.)

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Solution

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Official answer: 3.9 (±0.1) (±0.1)

Probability and Statistics

List the lengths of each of the 9 words in the sentence:

  1. "The" →3\rightarrow 3

  2. "quick" →5\rightarrow 5

  3. "brown" →5\rightarrow 5

  4. "fox" →3\rightarrow 3

  5. "jumps" →5\rightarrow 5

  6. "over" →4\rightarrow 4

  7. "the" →3\rightarrow 3

  8. "lazy" →4\rightarrow 4

  9. "dog" →3\rightarrow 3

Since each of the 9 pieces of paper has an equal probability of 19\frac{1}{9} being drawn, the expected length E[L]E[L] is the arithmetic mean of the word lengths:

E[L]=3+5+5+3+5+4+3+4+39=359≈3.8889E[L] = \frac{3 + 5 + 5 + 3 + 5 + 4 + 3 + 4 + 3}{9} = \frac{35}{9} \approx 3.8889

Rounding to one decimal place gives 3.9 (accepted range: 3.8 to 3.9).

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This Probability and Statistics previous year question is Q2 of the GATE CSE 2014 Set 2 paper. Find more GATE CSE PYQs on Probability and Statistics in Engineering Mathematics, or browse all GATE CSE PYQs.

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Probability and Statistics has 46 GATE CSE PYQs across 23 papers from 2011 to 2026. 11 of them are 1-mark NAT questions like this one, and GATE CSE 2014 Set 2 has 3.

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GateAI solution cardGATE CSE 2014 Set 2 · Q2 · NAT

Each of the nine words in the sentence "The quick brown fox jumps over the lazy dog" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The *expected length* of the word drawn is … (The answer should be rounded to one decimal place.)

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.