To determine the probability of rolling a number greater than three on a number cube, we need to follow a few logical steps.
1. Understand the Total Outcomes:
A standard number cube (like a die) has 6 faces, each showing one of the numbers: 1, 2, 3, 4, 5, and 6. Therefore, when you roll the cube, there are a total of 6 possible outcomes.
2. Identify the Favorable Outcomes:
We are interested in rolling a number greater than three. On a standard number cube, the numbers greater than three are 4, 5, and 6. Therefore, there are 3 favorable outcomes (the faces showing 4, 5, and 6).
3. Calculate the Probability:
The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability [tex]\( P \)[/tex] of rolling a number greater than three is given by the formula:
[tex]\[
P(\text{number} > 3) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\][/tex]
4. Apply the Numbers:
From our earlier identification:
- Number of favorable outcomes = 3 (faces showing 4, 5, and 6)
- Total number of outcomes = 6 (total faces on the number cube)
Substituting these values into the formula:
[tex]\[
P(\text{number} > 3) = \frac{3}{6}
\][/tex]
5. Simplifying the Fraction:
Simplify the fraction [tex]\( \frac{3}{6} \)[/tex]:
[tex]\[
\frac{3}{6} = 0.5
\][/tex]
So, the probability of rolling a number greater than three on a number cube is [tex]\( 0.5 \)[/tex] or 50%.
