Hello, I know this is probably simple but i just cant find out how to get the correct answer.
When P(A and B and C), How do i find just P(A and C) and also just P(B and C)?
Is there a formula to follow like the multiplication rule? I'm stumped.
Hello, I know this is probably simple but i just cant find out how to get the correct answer.
When P(A and B and C), How do i find just P(A and C) and also just P(B and C)?
Is there a formula to follow like the multiplication rule? I'm stumped.
Just brainstorming.
Only when events A, B and C are all independent of each other you can use the multiplication rule, thus having $\displaystyle P(A\cap B\cap C)=P(A)P(B)P(C).$ Otherwise you have use conditional probability which states that $\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}.$ From there you can write $\displaystyle P(A\cap B)=P(A|B)P(B).$
So you could write $\displaystyle P(A\cap B \cap C)=P(A|B\cap C)P(B\cap C)=P(A|B\cap C)P(B|C)P(C).$
See if this will get you started.