\(\therefore {\mkern 1mu} {\mkern 1mu} {{\text{P}}_{total}}{\text{   =   }}{{\text{p}}_{\text{A}}}^{\text{0}}{{\text{X}}_{\text{A}}}{\text{   +   }}{{\text{p}}_{\text{B}}}^{\text{0}}{{\text{X}}_{\text{B}}}\) \( = \left( {150 \times \frac{1}{2}} \right) + \left( {100 \times \frac{1}{2}} \right){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \) \( \Rightarrow {\mkern 1mu} {\mkern 1mu} {{\text{P}}_{total}}{\text{   =  }}{\mkern 1mu} {\mkern 1mu} {\text{125}}\)

\({{\text{p}}_{\text{B}}} = {Y_B} \times {{\text{P}}_{total }}\,\,\,\therefore \) \({Y_B} = \frac{{{p_B}}}{p} = \frac{{{p_B}^0{X_B}}}{p} = \left( {\frac{{100 \times \frac{1}{2}}}{{125}}} \right) = 0.4\)