So,I'm studying statistics (for engineers) now,and this is one of them courses that really gives me a headache time after time. Here for example,I can't seem to get the difference between P(A[itex]\bigcap[/itex]B),and P(A|B).I'l give an example in for of a question given to us in some class. "70 percent of students know statistics well.The probability that a student who doesn't know statistics well, answers statistics question in exam is 0.2 . Probability for a student who knows statistics well and answers statistics question correctly is 0.95. What is the probability of a random student who does know statistics well ,to answer the question wrong?" So,when they answered the question,they said that A-event of a student who knows statistics well. B-event that the student answered correctly. So,what we looking for is P(A[itex]\bigcap[/itex]Bc),as far as Ive understood.And yes,in the answer to the question it goes : P(A[itex]\bigcap[/itex]Bc)=P(Bc|A)*P(A)=0.05*0.7 Why why on earth why?? And why does P(A[itex]\bigcap[/itex]Bc)=P(A)-P(A[itex]\bigcap[/itex]B) does not work here?