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Let A,B, and C be events relating to the experiment of rolling a pair of dice.

(a) If

P(A|C) > P(B|C) and P(A|Cc) > P(B|Cc)

either prove that P(A) > P(B) or give a counterexample by defining events A,B, and C for which that relationship is not true.

(b) If

P(A|C) > P(A|Cc) and P(B|C) > P(B|Cc)

either prove that P(AB|C) > P(AB|Cc) or give a counterexample by defining events A,B, and C for which that relationship is not true.

Let C be the event that the sum of a pair of dice is 10; let A be the event that the first die lands on 6; let B be the event that the second die lands on 6.

(a) If

P(A|C) > P(B|C) and P(A|Cc) > P(B|Cc)

either prove that P(A) > P(B) or give a counterexample by defining events A,B, and C for which that relationship is not true.

(b) If

P(A|C) > P(A|Cc) and P(B|C) > P(B|Cc)

either prove that P(AB|C) > P(AB|Cc) or give a counterexample by defining events A,B, and C for which that relationship is not true.

Let C be the event that the sum of a pair of dice is 10; let A be the event that the first die lands on 6; let B be the event that the second die lands on 6.

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