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Math Help - How is the problem solved

  1. #1
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    How is the problem solved

    What equation was used to arrive at the solutions for this problem:
    Assume the probabilities of a nuclear/biological/chemical/radiological attack are independent. Using figures:
    P(nuke) = 0.1
    P(bio) = 0.2
    P(chem) = 0.2
    P(rad) = 0.3

    Then we can use the inclusion/exclusion rule to see that P(disaster in 5 years) = 0.6168
    and, make another assumption, that the average rate of attacks is 0.6168 per 5 years, then the distribution of time till the first attack, T ~ Exp(0.6168/5). so:
    P(attack this year | no attack in the last 4) = P(attack this year) = P(T < 1) = 0.1161
    The equation Iím using is:
    P(AUBuCuD) = P (A) + P (B) + P (C) + P (D) - P (A ∑ B) − P (A ∑ C) − P (A . D) − P (B ∑ C) − P (B ∑ D) − P (C ∑ D) + P(A . B . C . D)
    But, my answer is 0.5712.
    I donít know how this is converted to 5 years (Iíve tried P5= 1-(1-P)5
    Thank you for any comments
    LanceW
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  2. #2
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    Ah yes. thank you CB---seems I did not have the 3 at a time terms. So, I'm now using the following equation but I still don't receive the solution provide by the original person who stated the problem & solution:

    P(A and B and C and D)=P(A)+P(B)+P(C)+P(D)
    -P(A and B)-P(A and C)-P(A and D)-P(B and C)-P(B and D)-P(C and D)
    +P(A and B and C)+P(A and B and D)+P(A and C and D)+P(B and C and D)
    -P(A and B and C and D)

    Question: Should the last term (A and B and C and D) be a minus or a plus?

    Thanks for any comments
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lanceW View Post
    Ah yes. thank you CB---seems I did not have the 3 at a time terms. So, I'm now using the following equation but I still don't receive the solution provide by the original person who stated the problem & solution:

    P(A and B and C and D)=P(A)+P(B)+P(C)+P(D)
    -P(A and B)-P(A and C)-P(A and D)-P(B and C)-P(B and D)-P(C and D)
    +P(A and B and C)+P(A and B and D)+P(A and C and D)+P(B and C and D)
    -P(A and B and C and D)

    Question: Should the last term (A and B and C and D) be a minus or a plus?

    Thanks for any comments
    As it happens I don't get that answer either (but doing the calculation another way).

    CB
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  4. #4
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    Thanks for the help CB...

    The solution I receive now is 0.5968. Does that agree with your solution?
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by lanceW View Post
    Thanks for the help CB...

    The solution I receive now is 0.5968. Does that agree with your solution?
    Yes.

    CB
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  6. #6
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    Cool! Thanks again for your help
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