#### 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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Solution A Die is Thrown Three Times. Let X Be 'The Number of Twos Seen'. Find the Expectation of X. Concept: Bernoulli Trials and Binomial Distribution.