An urn contains 3 black and 5 red balls. If 3 balis are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is

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Aicharya · Accepted Answer

Let $X$ be number of red balls drawn. \begin{array}{|c|c|c|c|c|}\hline \boldsymbol{X}=\boldsymbol{x} & 0 & 1 & 2 & 3 \\\hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & \frac{{ }^3 C_3}{{ }^8 C_3} & \frac{{ }^5 C_1 \times{ }^3 C_2}{{ }^8 C_3} & \frac{{ }^5 C_1 \times{ }^3 C_1}{{ }^8 C_3} & \frac{{ }^5 C_3}{{ }^8 C_3} \\\hline\end{array} \begin{array}{|c|c|c|c|c|}\hline \boldsymbol{X}=\boldsymbol{x} & 0 & 1 & 2 & 3 \\\hline \boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x}) & \frac{1}{56} & \frac{15}{56} & \frac{30}{56} & \frac{10}{56} \\\hline\end{array}
Mean $=0 \times \frac{1}{56}+1 \times \frac{15}{56}+2 \times \frac{30}{56}+3 \times \frac{10}{56}=\frac{15}{8}$.

An urn contains 3 black and 5 red balls. If 3 balis are drawn at random from the urn, the mean of the…

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