find the probability of rolling a sum of 6 or 11 when rolling two number cubes. enter your response as a…

Explanation:

Step1: Find total number of outcomes

When rolling two number - cubes, each cube has 6 possible outcomes. So the total number of outcomes when rolling two cubes is $6\times6 = 36$.

Step2: Find number of ways to get a sum of 6

The possible pairs of numbers on the two cubes that sum to 6 are: $(1,5)$, $(2,4)$, $(3,3)$, $(4,2)$, $(5,1)$. So there are 5 ways to get a sum of 6.

Step3: Find number of ways to get a sum of 11

The possible pairs of numbers on the two cubes that sum to 11 are: $(5,6)$ and $(6,5)$. So there are 2 ways to get a sum of 11.

Step4: Use the addition rule for mutually - exclusive events

The events of getting a sum of 6 and getting a sum of 11 are mutually - exclusive. The number of favorable outcomes (sum of 6 or 11) is $5 + 2=7$. The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{7}{36}$.

Answer:

$\frac{7}{36}$