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# A Pair of Dice is Thrown 4 Times. If Getting a Doublet is Considered a Success, Find the Probability Distribution of the Number of Successes And, Hence, Find Its Mean. - CBSE (Science) Class 12 - Mathematics

ConceptRandom Variables and Its Probability Distributions

#### Question

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes and, hence, find its mean.

#### Solution

Let X be the number of times a doublet is obtained in four throws.
Then, p = probability of success in one throw of a pair of dice =

$\frac{6}{36} = \frac{1}{6}$

$\text{ and } q = \frac{5}{6}; n = 4$
$P(X = r) = ^ {4}{}{C}_r \left( \frac{1}{6} \right)^r \left( \frac{5}{6} \right)^{4 - r} , r = 0, 1, 2, 3, 4$
$\text{ As n = 4 and } p = \frac{1}{6},$
$\text{ mean } = np = \frac{4}{6} = \frac{2}{3}$

$\therefore P(X = r) =^ {4}{}{C}_r \left( \frac{5}{6} \right)^r \left( \frac{1}{6} \right)^{n - r} , r = 0, 1, 2, 3, 4$
$\text{ The distribution is as follows: }$

X             0      1     2      3      4
$P(X) \left( \frac{5}{6} \right)^4 \frac{20}{6^4} \frac{150}{6^4} \frac{500}{6^4} \frac{1}{6^4}$

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Solution A Pair of Dice is Thrown 4 Times. If Getting a Doublet is Considered a Success, Find the Probability Distribution of the Number of Successes And, Hence, Find Its Mean. Concept: Random Variables and Its Probability Distributions.
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