Jeff rolls a fair regular octahedral die marked with the numbers 1 through 8. Then Amelie rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?
+321 We can make a table:
1 2 3 4 5 6 7 8
1 1 2 3 4 5 6 7 8
2 2 4 6 8 10 12 14 16
3 3 6 9 12 15 18 21 24
4 4 8 12 16 20 24 28 32
5 5 10 15 20 25 30 35 40
6 6 12 18 24 30 36 42 48
We can see that in the table there are 48 values, and 24 of these are a multiple of three, so the probability that the product of the two rolls is a multiple of 3 is 24/48 = 1/2.
