A box contains $6$ red balls and $2$ black balls. Two balls are drawn at random from it without replacement. if $x$ denotes the number of red balls drawn, then find $E (x)$

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Solution

Total ball $= 6$ red $+ 2$ black $= 8$ ball
Total way to drawn two ball without replacement is
$\begin{matrix} \Rightarrow^{8} C_{2} = \frac{8!}{6! \times 2!} \frac{8 \times 7 \times 6!}{6! \times 2!} = \frac{8 \times 7}{2} = 28 S o E (x) = 28 \end{matrix}$

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