Results 1 to 2 of 2

Math Help - events

  1. #1
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35

    events

    21 . suppose that A,B and c are independent events .show that
    i. A and (A∩B) are independent.
    ii. A and (AUB) are independent.
    iii. Ac and (A∩cc) are independent.


    22. in a city ,25% of the cars emit pollutions to the air of the city .if a car failed to pass the emission of air pollutants with probability 0.99 and if a car that is not emitting air pollutants also fails the test with probability 0.17 .what is the probability that a car that fails the test actually emits air pollution ?

    23.the number of employees working in factories A,B and C are , respectively 50,75 and 100 . suppose that of those employees ,50% ,60 % and 70%,respectively ,are women .assuming that the probability of resignation is the same for men and women and that woman resigned ,what is the probability that she is from factory c ?

    24 . two balanced dice are rolled .if you know that the upper faces show different numbers ,what is the probability that one of the two faces show 4 .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    We know that from independence that P(AB) = P(A)P(B).
    Look at
    \begin{array}{rcl}<br />
 P(AB^c ) & = & P(A) - P(AB) \\  & = & P(A) - P(A)P(B) \\ <br />
  & = & P(A)\left( {1 - P(B)} \right) \\  & = & P(A)P(B^c ) \\ \end{array}
    That shows that A\,\& \,B^c are independent.

    By changing position B^c\,\& \,A, we see A^c\,\& \,B^c are independent.

    You do the other.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. independent events
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: June 2nd 2009, 03:03 PM
  2. Events
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 5th 2008, 04:35 AM
  3. events
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: July 15th 2008, 03:41 AM
  4. events
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 31st 2007, 04:20 PM
  5. Help two events
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 20th 2007, 04:41 PM

Search Tags


/mathhelpforum @mathhelpforum