So,I'm studying statistics (for engineers) now,and this is one of them courses that really gives me a headache time after time.(adsbygoogle = window.adsbygoogle || []).push({});

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]B^{c}),as far as Ive understood.And yes,in the answer to the question it goes :

P(A[itex]\bigcap[/itex]B^{c})=P(B^{c}|A)*P(A)=0.05*0.7

Why why on earth why??

And why does P(A[itex]\bigcap[/itex]B^{c})=P(A)-P(A[itex]\bigcap[/itex]B) does not work here?

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# Can't wrap my head around conditional probability

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