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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Can't wrap my head around conditional probability

**Physics Forums | Science Articles, Homework Help, Discussion**