Question

If XandY are independent binomial vatiates B(5, 1 2 )andB(7, 1 2 ) and the value of P(X+Y=3) is A. 35/47 B. 55/1024 C. 220/512 D. 11/204 Select the correct answer from above options

Answer 1

Correct Answer - B We, have P(X=r)=.5Cr( 1 2 )5and,P(Y=r)=.7Cr( 1 2 )7 Now, P(X+Y)=3)=P(X=0,Y=3)+P(X=1,Y=2)+P(X=2,Y=1)+P(X=3,Y=0) P ( X + Y ) = 3 ) = P ( X = 0 , Y = 3 ) + P ( X = 1 , Y = 2 ) + P ( X = 2 , Y = 1 ) + P ( X = 3 , Y = 0 ) =P(X=0)P(Y=3)+P(X=1)+P(Y=2)+P(X=2)P(Y=1)+P(X=3)P(Y=0) = P ( X = 0 ) P ( Y = 3 ) + P ( X = 1 ) + P ( Y = 2 ) + P ( X = 2 ) P ( Y = 1 ) + P ( X = 3 ) P ( Y = 0 ) =.5C0×( 1 2 )5×.7C3×( 1 2 )7+.5C1×( 1 2 )5×.C_2×( 1 2 )7 +.5C2×( 1 2 )5×.7C1×( 1 2 )7+.5C3×( 1 2 )5×.7C0×( 1 2 )7 =( 1 212 )(35+5×21+10×7+10×1)= 220 212 = 55 1024