quantum mechanics – Beam Splitter Toy Model History Weight Calculation

Given this modern of a beam splitter (see picture), and the two possible histories:

Yc = (0a) • (1c) • (2c) • (3c) • (4c)
And
Yd = (0a) • (1d) • (2d) • (3d) • (4d)
for f=4,

how do I calculate the weight of history Yc and Yd. I know Yc=Yd=0.5, but how do I calculate this? I hope I have provided enough information to answer this question. The material comes from Robert Griffiths “Consistent Quantum Theory” pg. 140-142.

Thank youbeam splitter toy model