anonymous
  • anonymous
P(EF') = P(E) - P(EF) Is it true or false? if its false how?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
is this probability?
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[P(E\cap F)=P(E)-F(E\cap F^c)\]?

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anonymous
  • anonymous
yeah so is it true?
anonymous
  • anonymous
yeah it is true
anonymous
  • anonymous
no not F(EF') its P(EF')
anonymous
  • anonymous
first of all by previous exercise we know that \[E=(E\cap F)\cup (E\cap F^c)\]
anonymous
  • anonymous
yeah that was as typo
anonymous
  • anonymous
oh ok lol
anonymous
  • anonymous
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 \[P((E\cap F)\cup (E\cap F^c))=P(E\cap F) +P (E\cap F^c)\]
anonymous
  • anonymous
therefore since the sets are the same, you have \[P(E)=P(E\cap F) +P (E\cap F^c)\]
anonymous
  • anonymous
ohh thank you
anonymous
  • anonymous
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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