A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 3 or 12?
+1622 A six sided dice has cases: 1, 2, 3, 4, 5, 6.
3 is prime, so you have to get a 1 and a 3 (2 cases)
12 has factors: (1, 12), (2, 6), (3, 4) (6 cases)
Total of 8 working cases. Total number of rolls is 6x6 = 36.
Probability is 8/36 = 2/9
1 - For product of 3, you have 2 possibilities: [1 x 3], [3 x 1]. Probability: 2 / 36 ==1 / 18
2 -For product of 12, you have 4 possibilites: [2 x 6], [6 x 2], [3 x 4], [4 x 3] ==4 / 36 ==1 / 9
3 - If you want to combine them, which you shouldn't because the question says: "3 OR 12", then: [2 +4] / 36= 1 /6
