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Probability: mutually exclusive vs. disjoint events

  1. Jan 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Are all disjoint events also mutually exclusive? And if events are independant does this also mean that they cannot be disjoint?

    2. Relevant equations

    no relevant equations

    3. The attempt at a solution

    In probability disjoint events are events that have no intersection. If the events have no intersection I would think that they would have to be mutually exclusive and could not be independant either because there is no way for them to both occur at the same time.
     
  2. jcsd
  3. Jan 25, 2007 #2
    mutually exclusive and disjoint are the same as you say the intersection is the empty set.

    Two events are independant if and only if P(A intersect B)=P(A).P(B) so again you are right mutually exclusive events cannot be independant and vice versa.

    Yo cannot throw a dice and get an odd number and an even number at the same time - mutually exclusive

    You can throw two dice and the probability of getting two sixes is 1/36 which is the probability of getting a six on one x probability of getting a six on the other - two dice are independant of each other

    P(6 & 6) =P(6).P(6)



    Throwing one die
    Probability of throwing an odd prime number {3,5} two out of six or 1/3

    P(odd number and a prime number) =1/3
    p(odd number) =1/2
    p(prime number) =1/2

    P(odd number and a prime number) not= p(odd number).P(prime number) so not independant events

    A number being prime is dependant on it being odd

    Hope this helps
     
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