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प्रश्न
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
उत्तर
Let X denote getting a number greater than 4 .
Then, X follows a binomial distribution with n=2
\[p = P(X > 4) = P(X = 5 \text{ or } 6)\]
\[ = \frac{1}{6} + \frac{1}{6}\]
\[ = \frac{1}{3}\]
\[q = 1 - p = \frac{2}{3}\]
\[P(X = r) = ^ {2}{}{C}_r \left( \frac{1}{3} \right)^r \left( \frac{2}{3} \right)^{2 - r} , r = 0, 1, 2 \]
\[\text{ Substituting for r we get probability distribution of X as follows } .\]
X 0 1 2
\[P(X) \frac{4}{9} \frac{4}{9} \frac{1}{9}\]
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