A foundry fab produces two batches of silicon wafers. Batch A yields 80% functional chips, while Batch B yields 60% functional chips. Due to volume differences, Batch A accounts for 70% of the fab's total output, and Batch B accounts for 30%. If you randomly select a functional chip from the final sorted bins, what is the mathematical probability that this specific chip originated from Batch B?
Instead of using formulas, imagine the fab produces exactly 100 total chips:
Batch A volume: 70 chips. At an 80% yield, that gives you 56 functional chips.
Batch B volume: 30 chips. At a 60% yield, that gives you 18 functional chips.
The final sorting bin now holds exactly 74 functional chips (56 + 18).
If you randomly grab one chip from that functional bin, the chance it belongs to Batch B is simply its share of the total good chips: 18 out of 74 (which simplifies to 9/37, or ~24.3%).
