Math

Let š“ , šµ , and š¶ be events associated with the same probabilistic model (i.e., subsets of a common sample space), and assume that š‘ƒ(š¶)>0 .

Decide whether the statement is True (always true), or False (not always true).

Suppose that š“āŠ‚š¶ . Then, š‘ƒ(š“āˆ£š¶)ā‰„š‘ƒ(š“) .

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  1. Consider this example
    A= rolling a 2
    S= rolling a die (1,2,3,4,5,6) are the outcomes
    C= rolling an even number (2,4,6)
    P(A) = 1 roll out of 6
    P(A given that C has occured which means a 2,4, or 6 is rolled) = 1/3
    Which is greater than the probability of A : )
    So TRUE for this example (with out given S)

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  2. all are true

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  3. Let A, B, and C be events associated with the same probabilistic model (i.e., subsets of a common sample space), and assume that P(C)>0.

    For each one of the following statements, decide whether the statement is True (always true), or False (not always true).

    Suppose that AāŠ‚C. Then, P(Aāˆ£C)ā‰„P(A).

    True
    False
    enviado

    Suppose that AāŠ‚B. Then, P(Aāˆ£C)ā‰¤P(Bāˆ£C).

    True
    False
    enviado

    Suppose that P(A)ā‰¤P(B). Then, P(Aāˆ£C)ā‰¤P(Bāˆ£C).

    True
    False
    enviado

    Suppose that AāŠ‚C, BāŠ‚C, and P(A)ā‰¤P(B). Then, P(Aāˆ£C)ā‰¤P(Bāˆ£C).

    True
    False

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