theorem Th51: :: RPR_1:51

for E being non empty finite set
for A, B1, B2, B3 being Event of E st 0 < prob B1 & 0 < prob B2 & 0 < prob B3 & (B1 \/ B2) \/ B3 = E & B1 misses B2 & B1 misses B3 & B2 misses B3 holds
prob A = (((prob (A,B1)) * (prob B1)) + ((prob (A,B2)) * (prob B2))) + ((prob (A,B3)) * (prob B3))