Question

Roll a die twice. Let A = {first roll is even}, B = {sum of two rolls is 4}. Find the conditional probability of A given B, and of B given A.  

Answer 1

When a die is rolled twice the sample space we obtained is:

S={ (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

The number of elements in the sample space are n(S)=36

Let A={first roll is even} and B = {sum of two rolls is 4}

therefore n(A)=18 n(B)=2

Therefore,

and  

  

(A and B)={(2,2)}

hence,

The conditional probability A given B is:

The conditional probability B given A is:

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