To determine the probability that Hannah rolls two number cubes and both numbers are greater than 3, let's break down the problem step by step.
1. Total Possible Outcomes:
Each number cube has 6 faces, numbered from 1 to 6. When rolling two number cubes, each cube operates independently, resulting in:
[tex]\[
6 \times 6 = 36 \text{ total possible outcomes}
\][/tex]
2. Identifying Favorable Outcomes:
To have both numbers greater than 3, each number on the cubes must be either 4, 5, or 6. Therefore, each cube has 3 possible favorable outcomes (4, 5, or 6).
3. Calculating Favorable Outcomes for Both Dice:
Since the outcomes on the number cubes are independent, we can determine the total favorable outcomes by multiplying the number of favorable outcomes for each die:
[tex]\[
3 \text{ (for the first die)} \times 3 \text{ (for the second die)} = 9 \text{ favorable outcomes}
\][/tex]
4. Calculating the Probability:
The probability of both numbers being greater than 3 is the ratio of the number of favorable outcomes to the total number of possible outcomes:
[tex]\[
\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{9}{36}
\][/tex]
Simplifying the fraction gives:
[tex]\[
\frac{9}{36} = \frac{1}{4}
\][/tex]
Thus, the probability that both numbers are greater than 3 is \(\frac{1}{4}\).
The correct answer is:
C) [tex]\(\frac{1}{4}\)[/tex]
