A die is thrown three times. Events A and B are defined as below: A :

1.	A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw; B : 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.
Answer» The sample space has 216 outcomes. Now A = (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4) (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4) (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,6,4) B = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)} and A ∩ B = {(6,5,4)}. Now, P(B) = 6/216 and P(A ∩ B) = 1/216 Then P(A/B) = (P(A ∩ B))/P(B) = (1/216)/(6/216) = 1/6

A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw; B : 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.

Answer»

The sample space has 216 outcomes.

Now A = (1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4) (3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4) (5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,6,4)

B = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}

and A ∩ B = {(6,5,4)}.

Now, P(B) = 6/216 and P(A ∩ B) = 1/216

Then P(A/B) = (P(A ∩ B))/P(B) = (1/216)/(6/216) = 1/6

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A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw; B : 6 on the first and 5 on the second throw. Find the probability of A given that B has already occurred.

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