Question

finding probabilities of compound events
second number cube
1 2 3 4 5 6
first number cube
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
what is the probability of rolling a sum of 10 when rolling two number cubes?
○ $\frac{1}{12}$
○ $\frac{1}{9}$
○ $\frac{1}{3}$
○ $\frac{5}{12}$

Explanation:

Step1: Find total number of outcomes

Each number - cube has 6 faces. When rolling two number - cubes, by the fundamental counting principle, the total number of outcomes is $6\times6 = 36$.

Step2: Find number of favorable outcomes

From the table, the pairs of numbers on the two cubes that sum to 10 are $(4,6)$, $(5,5)$, and $(6,4)$. So there are 3 favorable outcomes.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{3}{36}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$