'p1 = p1*0.1967 + p2*0.4561 + p3*0.3321 + p4*0.2982'
'p2 = p1*0.0750 + p2*0.0553 + p3*0.1986 + p4*0.0325'
'p3 = p1*0.2239 + p2*0.4863 + p3*0.0291 + p4*0.3382'
'p4 = p1*0.5044 + p2*0.0023 + p3*0.4402 + p4*0.3311'
'p1 + p2 + p3 + p4 = 1'
p1*(0.1967-1) + p2*0.4561 + p3*0.3321 + p4*0.2982 = 0
p1*0.0750 + p2*(0.0553-1) + p3*0.1986 + p4*0.0325 = 0
p1*0.2239 + p2*0.4863 + p3*(0.0291-1) + p4*0.3382 = 0