If two fair number cubes are rolled, what is P(1 and 2)?

That means the probability of getting one of these 2 rolls:

(1,2)  (2,1)

out of these 36 rolls:

(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)


That's a probability of 2 out of 36 or 
which reduces to 

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If two fair number cubes are rolled, what is P(1 and 2)?

That means the probability of getting one of these 18 rolls:

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

out of these 36 rolls:

(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)


That's a probability of 18 out of 36 or 
which reduces to