To solve the problem of finding the probability that Jacob gets a mule deer, let's go step-by-step through the given scenario:
1. Identify the number of mule deer (m):
Let's denote the number of mule deer as [tex]\( m \)[/tex]. For simplicity, we can assume [tex]\( m = 1 \)[/tex] since we are only interested in the ratio.
2. Determine the number of whitetail deer:
According to the problem, there are six times as many whitetail deer as mule deer. Therefore, if there is 1 mule deer, the number of whitetail deer is [tex]\( 6 \times m = 6 \times 1 = 6 \)[/tex].
3. Calculate the total number of deer:
The total number of deer in the woods is the sum of the mule deer and the whitetail deer.
[tex]\[
\text{Total number of deer} = m + 6m = 1 + 6 = 7
\][/tex]
4. Determine the probability of getting a mule deer:
The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. In this context, the favorable outcome is getting a mule deer.
[tex]\[
\text{Probability of getting a mule deer} = \frac{\text{Number of mule deer}}{\text{Total number of deer}} = \frac{m}{m + 6m} = \frac{1}{7}
\][/tex]
Therefore, the probability that Jacob gets a mule deer is
[tex]\[
\frac{1}{7}
\][/tex]
So, the correct answer is:
C. [tex]\(\frac{1}{7}\)[/tex]
