Results 1 to 2 of 2

Math Help - conditional probability proof

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    conditional probability proof

    Q: Show that P(T|D^{c})=1-P(T^{c}|D^{c})

    A:This is my path...

    P(T|D^{c})=\frac{P(T\cap\\D^{c})}{P(D^{c})}= <br />
\frac{P(T/D)}{P(D^{c})}=\frac{P(T)-P(T\cap\\D)}{P(D^{c})}=<br />
\frac{P(T)-P(D)P(T|D)}{P(D^{c})}= \frac{[P(T)-P(D)]P(T|D)}{P(D^{c})}=
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,669
    Thanks
    1618
    Awards
    1
    Here is what I would do.
    P(T|D^c ) = \frac{{P(T \cap D^c )}}<br />
{{P(D^c )}} = \frac{{P(D^c ) - P(T^c  \cap D^c )}}<br />
{{P(D^c )}} = 1 - P(T^c |D^c )
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. conditional probability proof
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: October 15th 2010, 06:21 PM
  2. conditional probability proof...
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 23rd 2010, 03:53 PM
  3. Conditional probability proof
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 11th 2010, 12:02 PM
  4. Conditional Probability Proof
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 22nd 2009, 10:37 AM
  5. conditional probability proof
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 6th 2008, 02:12 AM

Search Tags


/mathhelpforum @mathhelpforum