A. Show that if Pr(AIB)-Pr(AIB\") then Pr(A\"|B) = Pr(A\"IB\"). This means that

Question

A. Show that if Pr(AIB)-Pr(AIB") then Pr(A"|B) = Pr(A"IB"). This means that since if Pr(AIB) = Pr(A|B') is true only if A and B are independent we also have Pr(A"|B) = Pr(AIB') is true only if A and B are independent. B. Show that if Pr(AIB) = Pr(A) then Pr(AIB) = Pr(A"). This means that since if Pr(A|B) = Pr(A) is true only if A and B are independent we also have Pr(AIB) = Pr(A*) is only true if A and B are independent. C. Suppose we roll a six-sided die and define the following events. A = get an even number, so get 2 or 4 or 6 B=get a number less than 4, so get 1 or 2 or 3 Are A and B independent? Justify your answer

Explanation / Answer

C) When we roll a die we get the following output

S ={1,2,3,4,5,6}

A = The even numbers set {2,4,6}

B= Less than 4 {1,2,3}

From both the sets the common vale is 2

So A and B are not independent since there is a common element 2.

So A and B aredependent events.

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