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mathmath333

  • one year ago

Probablity Question

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  1. mathmath333
    • one year ago
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    Check whether the following probabilities P(A) and P(B) are consistently defined (i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6 (ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8

  2. mathmath333
    • one year ago
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    i found an answer here but it doesn't making sense to me http://www.meritnation.com/ask-answer/question/check-whether-the-following-probabilities-p-a-and-p-b-are/probability/6322947

  3. Vocaloid
    • one year ago
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    in order to be consistently defined: P(A ∩ B) must be less than or equal to P(A) and P(B) P(A ∪ B) must be greater than or equal to P(A) and P(B)

  4. mathmath333
    • one year ago
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    u mean both conditions or any one condition should be satisfied

  5. Vocaloid
    • one year ago
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    both

  6. Vocaloid
    • one year ago
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    so, for the first one (i) what do you think the answer is? (i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6

  7. mathmath333
    • one year ago
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    consistentlyt defined

  8. Vocaloid
    • one year ago
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    not quite, check the first condition again... P(A ∩ B) must be less than or equal to P(A) and P(B)

  9. Vocaloid
    • one year ago
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    notice how P(A ∩ B) is greater than P(B)?

  10. Zarkon
    • one year ago
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    these "P(A ∩ B) must be less than or equal to P(A) and P(B) P(A ∪ B) must be greater than or equal to P(A) and P(B)" are necessary conditions but not sufficient

  11. mathmath333
    • one year ago
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    i am confused

  12. anonymous
    • one year ago
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    |dw:1439556261906:dw|

  13. anonymous
    • one year ago
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    The second one is possible, since they can overlap 0.2 to get A U B = 0.8 |dw:1439556485375:dw|

  14. anonymous
    • one year ago
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    |dw:1439556527719:dw|

  15. anonymous
    • one year ago
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    That makes the expression hold.

  16. Zarkon
    • one year ago
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    for example you can't have P(A)=.8 , P(B)=.9 and P(A\(\cap\)B)=0 and you can't have P(A)=.2 , P(B)=.3 and P(A\(\cup\)B)=.8 they satisfy "P(A ∩ B) must be less than or equal to P(A) and P(B) P(A ∪ B) must be greater than or equal to P(A) and P(B)" but they are not consistently defined

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