Probability and conditional information

For 10,000 modelled items, compare defective rates of 1% and 10%. In both populations a scanner flags 90% of defective items and 5% of nondefective items. Predict how the defective share among flagged items will change before building expected-count tables. Label the conditioning group in every fraction, and check the result using disjoint paths in a tree. Explain why a flag rate among defective items cannot simply be reversed.