To find the probability that an animal is female, given that it is a chicken, we start by analyzing the relevant information provided in the table.
Here we are dealing only with the chicken population on the farm.
Firstly, we need to determine the total number of chickens on the farm. The table shows:
- There are [tex]\(2\)[/tex] male chickens.
- There are [tex]\(13\)[/tex] female chickens.
So, the total number of chickens is the sum of the male and female chickens:
[tex]\[
\text{Total chickens} = \text{Male chickens} + \text{Female chickens} = 2 + 13 = 15
\][/tex]
Next, to find the probability that a chicken chosen at random is female (i.e., [tex]\( P(\text{Female} \mid \text{Chicken}) \)[/tex]), we use the ratio of the number of female chickens to the total number of chickens.
Given:
[tex]\[
P(\text{Female} \mid \text{Chicken}) = \frac{\text{Number of female chickens}}{\text{Total number of chickens}}
\][/tex]
Substituting the values we found:
[tex]\[
P(\text{Female} \mid \text{Chicken}) = \frac{13}{15}
\][/tex]
Thus the probability that the selected chicken is female is:
[tex]\[
P(\text{Female} \mid \text{Chicken}) = \frac{13}{15} \approx 0.8667
\][/tex]
Therefore, the probability that an animal is female given that it is a chicken is approximately [tex]\(0.8667\)[/tex] or [tex]\(86.67\%\)[/tex].
