Pulsified333
  • Pulsified333
about independent events E and F in a sample space S, but assume that Pr[E]=0.2 and Pr[F]=0.4. Compute the following conditional probabilities: (1) Pr[E′|F]= (2) Pr[E|F′]=
Mathematics
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Pulsified333
  • Pulsified333
about independent events E and F in a sample space S, but assume that Pr[E]=0.2 and Pr[F]=0.4. Compute the following conditional probabilities: (1) Pr[E′|F]= (2) Pr[E|F′]=
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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misty1212
  • misty1212
if they are independent, then multiply
Pulsified333
  • Pulsified333
hello again :D
misty1212
  • misty1212
hi!!

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Pulsified333
  • Pulsified333
but what happens if its the complement of one of them
misty1212
  • misty1212
if they are independent then \[P(E'|F)=P(E')P(F)\]
Pulsified333
  • Pulsified333
oh sweet :D
misty1212
  • misty1212
should be pretty clear that if the events are independent, then so are the compliments etc q
Pulsified333
  • Pulsified333
that didn't work
Pulsified333
  • Pulsified333
misty1212
  • misty1212
hmm i see my mistake
Pulsified333
  • Pulsified333
oh
misty1212
  • misty1212
to find\[P(E'|F)=\frac{P(E'\cap F)}{P(F)}=\frac{P(E')P(F)}{P(F)}=P(E')\] which is a silly way of saying that if E' and F are independent then \(P(E'|F)=P(E')\)

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