Question

arturo rolls two six - sided number cubes, with faces labeled 1 - 6, as shown in the figure.

1. what is the probability that the sum of the numbers on the two cubes is 6?

a. $\frac{1}{36}$
b. $\frac{5}{36}$
c. $\frac{5}{18}$
d. $\frac{7}{12}$

1. what is the probability that the product of the numbers on the two cubes is 6?

a. $\frac{1}{18}$
b. $\frac{1}{9}$
c. $\frac{1}{6}$
d. $\frac{1}{2}$

Explanation:

Step1: Find total number of outcomes

When rolling two six - sided dice, the total number of outcomes is $6\times6 = 36$ since each die has 6 possible results.

Step2: Find favorable outcomes for sum equal to 6

The pairs of numbers on the two dice that sum to 6 are: $(1,5),(2,4),(3,3),(4,2),(5,1)$. So there are 5 favorable outcomes.

Step3: Calculate probability for sum equal to 6

The probability $P(\text{sum}=6)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{5}{36}$.

Step4: Find favorable outcomes for product equal to 6

The pairs of numbers on the two dice that have a product of 6 are: $(1,6),(2,3),(3,2),(6,1)$. So there are 4 favorable outcomes.

Step5: Calculate probability for product equal to 6

The probability $P(\text{product}=6)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{4}{36}=\frac{1}{9}$.

Answer:

1. B. $\frac{5}{36}$
2. B. $\frac{1}{9}$