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Probability Question experiment

  1. Sep 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose that an experiment has five possible outcomes, which are denoted {1,2,3,4,5}. Let A be the Event {1,2,3} and let B be the event {3,4,5}. (Notice that we did not say that the five outcomes are equally likely: The probability distributions could be anything.) For each of the following relations, tell whether it could possibly hold.

    If it could, give a numerical example using a probability distribution of your own choice; if it could not, explain why not (what rule is violated).

    a. P(A) = P(B)
    b. P(A) = 2P(B)
    c. P(A) = 1 - P(B)
    d. P(A) + P(B) > 1
    e. P(A) - P(B) < 0
    f. P(A) - P(B) > 1

    2. Relevant equations



    3. The attempt at a solution


    I am honestly not sure If I am doing these right, so please correct me if I am in the wrong direction.

    a. P(A) = P(B)
    Can Hold: Example if set is uniformly distributed.
    P(A) = .6 = P(B)

    b. P(A) = 2P(B)
    Can hold:
    P(1)=.35
    P(2)=.3
    P(3)=.05
    P(4)=.15
    P(5)=.15

    .7 = .7

    c. P(A) = 1 - P(B)
    P(A) = P(1) + P(2) +P(3), P(B') = P(1) + P(2)
    This holds if P(3) = 0

    d. P(A) + P(B) > 1
    Can hold if uniformly distributed.
    .6+.6 = 1.2

    e. P(A) - P(B) < 0
    Can hold: P(1) = .1, P(2) = .1, P(3) = .2, P(4) = .3, P(5) = .3
    P(A)= .4, P(B)=.8
    P(A) - P(B) = -.4

    f. P(A) - P(B) > 1
    Can not hold. P(A) & P(B) are both between 1 and 0. Using extreme points 1-1 = 0, 0-1 = -1, 1-0 = 1.
     
    Last edited: Sep 13, 2013
  2. jcsd
  3. Sep 13, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    They are all right.
     
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