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  • An urn contains 5 red, 2 white and 3 black balls. Three balls are drawn, one-by-one, at random without replacement. Find the probability distribution of the number of white balls. Also, find the mean and the variance of the number of whi

An urn contains 5 red, 2 white and 3 black balls. Three balls are drawn, one-by-one, at random without replacement. Find the probability distribution of the number of white balls. Also, find the mean and the variance of the number of white balls drawn.

 

Answers (1)

Assume the number of white balls are X.

X = 0,1,2

X p(X) X.p(X) X2.p(X)
0 \frac{8}{10} \times \frac{7}{9} \times \frac{6}{8}=\frac{7}{15} 0 0
1 3 \times \frac{8}{10} \times \frac{7}{9} \times \frac{2}{8}=\frac{7}{15} \frac{7}{15} \frac{7}{15}
2 3 \times \frac{8}{10} \times \frac{2}{9} \times \frac{1}{8}=\frac{1}{15} \frac{2}{15} \frac{4}{15}

\\ \text { Mean }=\sum X p(X) \\ = \frac{7}{15}+\frac{2}{15} \\\\ =\frac{3}{5} \\

\\ \text { Variance }=\sum X^{2} p(x)-\left[\sum X p(X)\right]^2 \\\\ =\frac{7}{15} + \frac{4}{15} - \left[\frac{3}{5}\right]^{2}\\\\ =\frac{11}{15} - \frac{9}{25} \\\\ = \frac{55-27}{75} = \frac{28}{75}

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Safeer PP

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