# 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(š¶)>0 .

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

Suppose that š“āš¶ . Then, š(š“ā£š¶)ā„š(š“) .

1. 👍 3
2. 👎 0
3. 👁 1,298
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)

1. 👍 1
2. 👎 0
2. all are true

1. 👍 1
2. 👎 0
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 AāC. Then, P(Aā£C)ā„P(A).

True
False

Suppose that AāB. Then, P(Aā£C)ā¤P(Bā£C).

True
False

Suppose that P(A)ā¤P(B). Then, P(Aā£C)ā¤P(Bā£C).

True
False

Suppose that AāC, BāC, and P(A)ā¤P(B). Then, P(Aā£C)ā¤P(Bā£C).

True
False

1. 👍 0
2. 👎 0

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