To solve the question of finding the probability of the complement of rolling a number less than 5 when using a six-sided die, we can follow these steps:
1. Identify the total number of possible outcomes:
A standard six-sided die has the numbers 1 through 6 on its faces. Therefore, there are a total of 6 possible outcomes when rolling this die.
2. Identify the event of interest:
We are interested in the event of rolling a number less than 5. The numbers that are less than 5 on a six-sided die are 1, 2, 3, and 4. Hence, there are 4 favorable outcomes for rolling a number less than 5.
3. Calculate the probability of the event:
The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. Thus, the probability of rolling a number less than 5 is:
[tex]\[
\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3}
\][/tex]
4. Determine the complement of the event:
The complement of the event "rolling a number less than 5" is the event "rolling a number that is not less than 5". The numbers on the die that are not less than 5 are 5 and 6.
5. Calculate the probability of the complement:
Since the sum of the probabilities of an event and its complement is always 1, the probability of the complement is:
[tex]\[
1 - \text{Probability of event} = 1 - \frac{2}{3} = \frac{1}{3}
\][/tex]
Therefore, the probability of the complement of rolling a number less than 5 on a six-sided die is:
[tex]\[
\boxed{\frac{1}{3}}
\][/tex]
This matches one of the provided options, confirming the answer is correct.
