Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# A Die is Thrown Three Times. Let X Be 'The Number of Twos Seen'. Find the Expectation of X. - Mathematics

#### Question

A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.

#### Solution

$\text{ We have } ,$
$p = \text{ probability of getting a number two in a throw } = \frac{1}{6} \text{ and }$
$q = 1 - p = 1 - \frac{1}{6} = \frac{5}{6}$
$\text{ As, X denote 'the number of twos seen } ' .$
$\text{ So, X follows binomial distribution with parameters n = 3 and } p = \frac{1}{6}$
$\therefore E\left( X \right) = np = 3 \times \frac{1}{6} = \frac{1}{2}$

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