Two dice are thrown. Find the probability that the number appeared has

1.	Two dice are thrown. Find the probability that the number appeared has a sum 8 if it is known that the second dice always exhibits 4?
Answer» Let A be an event of always 4 exhibits on second dice i.e., A = {(1,4),(2,4),(3,4),(4,4),(5,4),(6,4)} n(A) = 6 and B be an event of the numbers appeared has a sum of 8 i;e., B = {(4,4)} ∴ A ∩ B = {(4,4)} ∴ n(A ∩ B) = 1 Hence, P(B/A) = n(A ∩ B)/n(A) = 1/6

Two dice are thrown. Find the probability that the number appeared has a sum 8 if it is known that the second dice always exhibits 4?

Answer»

Let A be an event of always 4 exhibits on second dice

i.e., A = {(1,4),(2,4),(3,4),(4,4),(5,4),(6,4)}

n(A) = 6

and B be an event of the numbers appeared has a sum of 8

i;e., B = {(4,4)}

∴ A ∩ B = {(4,4)}
∴ n(A ∩ B) = 1

Hence, P(B/A) = n(A ∩ B)/n(A) = 1/6