a.) Find the probability that the second dice is 4 or the sum of the dice is 7.
Here are the 36 dice 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)
If we erase all but those with the second dice 4 or the
sum of the dice is 7:
(1,4) (1,6)
(2,4) (2,5)
(3,4)
(4,3) (4,4)
(5,2) (5,4)
(6,1) (6,4)
Count them. That's 11. Probability = 11/36.
b.) Find the probability that the first dice is 3 or that doubles are rolled.
Here are the 36 dice rolls again:
(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)
I'll erase all but the ones with the first dice 3 or doubles:
(1,1)
(2,2)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,4)
(5,5)
(6,6)
Count them. There's also 11 of those. Probability = 11/36.
Edwin