Alright, let's break down the given problem in a step-by-step manner.
We need to determine the probability that a selected animal is a female, given that it is a sheep from the table provided. Here's how we do it:
1. Identify the relevant numbers from the table:
- The number of male sheep is 2.
- The number of female sheep is 13.
2. Calculate the total number of sheep:
- Total number of sheep = Number of male sheep + Number of female sheep
- Total number of sheep = 2 (male sheep) + 13 (female sheep)
- Total number of sheep = 15
3. Probability formula application:
- We need to use the formula for conditional probability, which is stated as:
[tex]\[
P(\text{Female} \mid \text{Sheep}) = \frac{P(\text{Female and Sheep})}{P(\text{Sheep})}
\][/tex]
- Here, [tex]\(P(\text{Female and Sheep})\)[/tex] is the probability of selecting a female sheep, which can be calculated by dividing the number of female sheep by the total number of sheep.
[tex]\[
P(\text{Female and Sheep}) = \frac{\text{Number of female sheep}}{\text{Total number of sheep}} = \frac{13}{15}
\][/tex]
- Since any selected animal from the group must be a sheep (given in the problem), [tex]\(P(\text{Sheep})\)[/tex] is 1.
4. Calculate the conditional probability:
- [tex]\[
P(\text{Female} \mid \text{Sheep}) = \frac{13}{15}
\][/tex]
Thus, the probability that the selected animal is a female, given that it is a sheep, is [tex]\(\frac{13}{15}\)[/tex], which is approximately 0.8667 or 86.67%.
