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)

• A. 3.88

Answer 1

The correct option is A 3.88

Let X = length of the word drawn.

So X can take only 3 values i.e.
X = {3, 4, 5}

So Prob distribution;

$X$	$3$	$4$	$5$
$P\left(X\right)$	$\frac{4}{9}$	$\frac{2}{9}$	$\frac{3}{9}$

Expected length $=E\left(X\right)=\sum p_i{x}_i$

$=p_1{x}_1+p_2{x}_2+p_3{x}_3$

$=(3\times \frac{4}{9})+(4\times \frac{2}{9})+(5\times \frac{3}{9})=3.88$