1. ## Simple Probability Question

I've been trying to solve this for a few minutes and checking the rules in my book back and forth but I can't seem to understand why. P(A ∩ B) - P(A ∩ B^c) = P(A)?

here are my calculations in which I need to find P(A)

below are the correction from the book which also says P(A ∩ B) - P(A ∩ B^c) = P(A). I thought it was only P(A ∩ B) + P(A ∩ B^c) = P(A)?

2. ## Re: Simple Probability Question

Originally Posted by steelmaste
I've been trying to solve this for a few minutes and checking the rules in my book back and forth but I can't seem to understand why. P(A ∩ B) - P(A ∩ B^c) = P(A)?
You are correct. I would say that is a typo in your textbook.
It is $\mathcal{P}(A)=\mathcal{P}(A\cap B){\bf\large{+}}\mathcal{P}(A\cap B^c)$

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