Truth table of probabilities:
- Does study/gets A: 0.8*0.5=0.4, 40%
- Does study/fails A: 0.2*0.5=0.1, 10%
- Doesn't study/gets A: 0.1*0.5=0.05, 5%
- Doesn't study/fails A: 0.9*0.5=0.45, 45%
There is a 40% probability that Jose studies and gets an A, where the probability is determined before the test. However, given that he gets an A, which is certain, the probability that he studied to get it remains at 50% if judging after the test when the results were known.