GATE CS 2014 Set 2 — Question 12
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Engineering Mathematics → Probability & Statistics → Elementary Statistics & Probability
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Question
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.)
Correct answer
3.8 to 3.9
Solution
To find the expected length of a word drawn at random, we use the formula for expected value , where is the length of each word and is the probability of drawing that word.Step 1: List the words and their lengths from the sentence "The quick brown fox jumps over the lazy dog":
Step 2: Count the total number of words ().
Step 3: Calculate the sum of the lengths of all words.
Step 4: Since each word is drawn at random with equal probability, for each word.
Step 5: Round the result to one decimal place as specified in the question.
The official answer key accepts a range from 3.8 to 3.9.
| Word | Length () |
|---|---|
| The | 3 |
| quick | 5 |
| brown | 5 |
| fox | 3 |
| jumps | 5 |
| over | 4 |
| the | 3 |
| lazy | 4 |
| dog | 3 |
Step 3: Calculate the sum of the lengths of all words.
Step 4: Since each word is drawn at random with equal probability, for each word.
Step 5: Round the result to one decimal place as specified in the question.
The official answer key accepts a range from 3.8 to 3.9.
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