To find the probability of drawing a card that is a factor of 8 from the set \( {5, 6, 7, 8} \), we first identify the factors of 8. The factors of 8 are:
- 1
- 2
- 4
- 8
Now, we'll check each card in the set \( {5, 6, 7, 8} \):
- 5 is not a factor of 8.
- 6 is not a factor of 8.
- 7 is not a factor of 8.
- 8 is a factor of 8.
So, only the card with the number 8 is a factor of 8.
Next, we determine the total number of outcomes, which is the total number of cards, and the number of favorable outcomes, which is the number of cards that are factors of 8.
- Total number of cards = 4 (5, 6, 7, 8)
- Number of favorable outcomes (factors of 8) = 1 (only the card 8)
Now we can find the probability \( P \):
\[ P(\text{factor of 8}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{4} \]
Thus, the probability of picking a factor of 8 is \( \frac{1}{4} \).