P(EF') = P(E) - P(EF) Is it true or false? if its false how?

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P(EF') = P(E) - P(EF) Is it true or false? if its false how?

Mathematics
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is this probability?
yes
\[P(E\cap F)=P(E)-F(E\cap F^c)\]?

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Other answers:

yeah so is it true?
yeah it is true
no not F(EF') its P(EF')
first of all by previous exercise we know that \[E=(E\cap F)\cup (E\cap F^c)\]
yeah that was as typo
oh ok lol
and since \[E\cap F\] and \[E\cap F^c\] are disjoint, the probability of their union is the sum of their probabilities, that is \[P((E\cap F)\cup (E\cap F^c))=P(E\cap F) +P (E\cap F^c)\]
therefore since the sets are the same, you have \[P(E)=P(E\cap F) +P (E\cap F^c)\]
ohh thank you
if you think about what this says in english it is obvious. you are interested in the probability of E so you know you are in the set E. now if you are in E either you are in F or you are not in F those are the logical possibilities. so \[E=(E\cap F)\cup (E\cap F^c)\]

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