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Question
A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.
Solution
Let X denote the number of white balls when 2 balls are drawn from the bag.
X follows a distribution with values 0,1 or 2.
\[P(X = 0) = P(\text{ All balls non - white } ) = \frac{^{7}{}{C}_2}{^{9}{}{C}_2} = \frac{42}{72} = \frac{21}{36}\]
\[P(X = 1) = P \hspace{0.167em} ( Ist \hspace{0.167em}\text{ ball white and IInd ball non - white } ) \hspace{0.167em} \]
\[ = \frac{^{7}{}{C}_1 ^{2}{}{C}_1}{^{9}{}{C}_2} = \frac{14}{36}\]
\[P(X = 2) = P( \text{ Both balls white} ) = \frac{^{2}{}{C}_2}{^{9}{}{C}_2} = \frac{1}{36}\]
\[\text{ It can be shown in tabular form as follows . } \]
X 0 1 2
\[P(X) \ \ \frac {21}{36} \frac{14}{36} \frac{1}{36}\]
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