To find the probability that Danl rolls a number less than 3 and subsequently the complement of this probability, follow these steps:
1. Identify the total number of sides on the die:
- The die has 8 sides, numbered from 1 through 8.
2. Calculate the probability of rolling any single number:
- Each side has an equal chance of landing face up, so the probability of rolling any specific number (say the number 1) is [tex]\( \frac{1}{8} \)[/tex].
3. Determine the favorable outcomes:
- We are interested in rolling a number less than 3. The numbers less than 3 are 1 and 2.
- Therefore, there are 2 favorable outcomes.
4. Calculate the probability of rolling a number less than 3:
- There are 2 favorable outcomes out of a total of 8 possible outcomes.
- The probability, [tex]\( P(A) \)[/tex], of rolling a number less than 3 is [tex]\( \frac{\text{number of favorable outcomes}}{\text{total number of sides}} = \frac{2}{8} = \frac{1}{4} \)[/tex].
5. Calculate the probability of the complement event [tex]\( P(A^c) \)[/tex]:
- The complement event [tex]\( P(A^c) \)[/tex] represents the probability of rolling a number that is not less than 3.
- The probability of the complement event is [tex]\( P(A^c) = 1 - P(A) \)[/tex].
- Using the probability [tex]\( P(A) = \frac{1}{4} \)[/tex], we find:
[tex]\[
P(A^c) = 1 - \frac{1}{4} = \frac{3}{4}
\][/tex]
Thus, the probability that Danl rolls a number that is not less than 3 is [tex]\( \frac{3}{4} \)[/tex].
So, the correct answer is [tex]\( \frac{3}{4} \)[/tex].
