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If `X and Y` are independent binomial vatiates `B(5,1/2) and B(7,1/2)` and the value of `P(X+Y=3)` isA. `(35)/(47)`B. `(55)/(1024)`C. `(220)/(512)`D. `(11)/(204)` |
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Answer» Correct Answer - B For X binomial variate `B(5,(1)/(2))` `rArr p=(1)/(2), n=5,q=(1)/(2)` For Y binomial variate `B(7,(1)/(2))` `rArr p=(1)/(2), n=7,q=(1)/(2)` Now, `X+Y=3` (i) When `X=0,Y=3` , possible cases `=.^(5)C_(0)((1)/(2))^5 .^(7)C_(3)((1)/(2))^2=35((1)/(2))^12` (ii) When `X=1,Y=2`, possible cases `=.^(5)C_(1)((1)/(2))^(5).^(7)C_(2)((1)/(2))^2=106((1)/(2))^12` (iii) When `X=2,Y=1`, possible cases `=.^(5)C_(2)((1)/(2))^(5) .^(7)C_(1)((1)/(2))^(7) =70 ((1)/(2))^12` (iv) When `X=3,Y=0` possible cases `= .^(5)C_(3)((1)/(2))^(2).^(7)C_(0)((1)/(2))^2=10((1)/(2))^(12)` `therefore` Total cases `=((1)/(2))^(12)xx[35+105+70+10]` `=(220)/(2^12)=(55)/(1024)` . |
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