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.)

Answer 1

Concept:

Expected length E(X) = ∑ (X × P(X))

where X is random variable denoting length of word drawn

Explanation:

word	Length
The	3
quick	5
brown	5
fox	3
jumps	5
over	4
the	3
lazy	4
dog	3

 

Each of the nine words has equal probability.

\(\frac{1}{9}\left( {3 + 5 + 5 + 3 + 5 + 4 + 3 + 4 + 3} \right) = \frac{{35}}{9} = 3.9\) 

Hence 3.9 is the expected length.