A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 3 or 12?

Guest Mar 13, 2023

#1**0 **

To find the probability that the product of the rolls is 3 or 12, we can first list all the possible outcomes of rolling the die twice and calculate the product of each outcome:

1 × 1 = 1

1 × 2 = 2

1 × 3 = 3

1 × 4 = 4

1 × 5 = 5

1 × 6 = 6

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10

2 × 6 = 12

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

4 × 1 = 4

4 × 2 = 8

4 × 3 = 12

4 × 4 = 16

4 × 5 = 20

4 × 6 = 24

5 × 1 = 5

5 × 2 = 10

5 × 3 = 15

5 × 4 = 20

5 × 5 = 25

5 × 6 = 30

6 × 1 = 6

6 × 2 = 12

6 × 3 = 18

6 × 4 = 24

6 × 5 = 30

6 × 6 = 36

We can see that the only outcomes that have a product of 3 or 12 are:

1 × 3 = 3

3 × 1 = 3

2 × 6 = 12

6 × 2 = 12

Therefore, out of the 36 possible outcomes, there are only 4 outcomes that have a product of 3 or 12. Therefore, the probability of rolling a product of 3 or 12 is:

P(product is 3 or 12) = 4/36 = 1/9

Therefore, the probability that the product of the rolls is 3 or 12 is 1/9 or approximately 0.111.

Justingavriel1233 Mar 13, 2023