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(True/False) Basic Probability Theory

  1. Mar 11, 2009 #1
    Dear all,

    I have a question.

    Suppose we have 3 events X,Y,Z defined as having 200 heads, 400 heads & 600 heads obtained in tossing a fair coin for 800 times.

    Then, P(Z)=P(X+Y)=P(600)=P(200+400)=P(X)+P(Y)=P(200)+P(400)

    The answer is false but I view it otherwise. My argument is based on the idea of the union of 2 events -> P(X U Y) =P(X) + P(Y). Following this line of reasoning, why is the above statement not considered true?

    Please kindly elaborate and direct me to the right understanding level.

    Thanks in advance.

    Regards
    Rela
     
  2. jcsd
  3. Mar 11, 2009 #2

    tiny-tim

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    Hi Rela! :smile:

    P(Z) is the probability of exactly 600 heads …

    in full, P(Z) = P({600 heads and 200 tails}) …

    so is the statement P({600 heads and 200 tails}) = P({400 heads and 400 tails} U {200 heads and 600 tails}) true or false or meaningless? :wink:
     
  4. Mar 12, 2009 #3
    Hi Tim,

    Many thanks for your prompt revert.

    Hmmm...It looks kinda meaningless to me. But I'm just perturbed by the fact that there exists such a rule in which the probability of the union of 2 statistically events A & B is the the sum of their individual probabilities (i.e P(AUB)=P(A)+P(B).

    I just feel that I could apply this rule to the problem statement defined earlier since it makes sense mathematically.

    Are you able to elaborate more on the circumstance in which I could apply the above rule correctly then?

    Regards
    Rela
     
  5. Mar 12, 2009 #4

    tiny-tim

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    Hi Rela! :smile:
    Yes, that's right … it's meaningless! :biggrin:
    The probability of the union of 2 distinct (non-overlappping) events A & B is the the sum of their individual probabilities.

    (and the probability of the intersection of 2 independent events A & B is the the product of their individual probabilities :wink:)
    yes … you could use the rule if X is exactly 200 heads, Y is exactly 400 heads, and Z is exactly either 200 or 400 heads. :smile:

    (because X and Y are distinct … ie, they don't overlap … and Z is their union)
     
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