The expected value of juniors in the committee will be "0.9".
According to the question,
A committee is to have three members from 9 juniors as well as 21 senior members.
The total ways of choosing three members, then
The expected value of juniors in the committee is:
= [tex]\Sigma x_i P(x = x_i)[/tex]
= [tex]0.P(x =0)+1.P(x=1)+2.P(x=2)+3.P(x=3)[/tex]
= [tex]0+\frac{9C_1.21_C_2}{30_C_3} + 2.\frac{9C_2.21_C_1}{30_C_3}+3.\frac{9C_3.21_C_2}{30_C_3}[/tex]
= [tex]\frac{1}{30_C_3} [\frac{9\times 21\times 20}{2} +\frac{2\times 9\times 8\times 21}{2} +\frac{3\times 9\times 8\times 7\times 21}{3\times 2\time 21} ][/tex]
= [tex]\frac{1}{30_C_3}[1890+2\times 756+3.84][/tex]
= [tex]\frac{3654}{30_C_3}[/tex]
= [tex]\frac{9}{10}[/tex]
or,
= [tex]0.9[/tex]
Thus the above response is correct.
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