To determine the probability that an animal is a male given that it is a pig, we will use conditional probability. Specifically, we will apply the formula for conditional probability:
[tex]\[ P(\text{Male} \mid \text{Pig}) = \frac{P(\text{Male and Pig})}{P(\text{Pig})} \][/tex]
Let's break this down step by step.
1. Determine the number of male pigs:
According to the table, there are [tex]\( 5 \)[/tex] male pigs.
2. Determine the number of female pigs:
According to the table, there are [tex]\( 5 \)[/tex] female pigs.
3. Calculate the total number of pigs:
The total number of pigs is the sum of male pigs and female pigs.
[tex]\[ \text{Total number of pigs} = 5 \ (\text{male pigs}) + 5 \ (\text{female pigs}) = 10 \][/tex]
4. Find the probability of selecting a pig ( [tex]\( P(\text{Pig}) \)[/tex] ):
Since we are considering only pigs and the total number of pigs is [tex]\( 10 \)[/tex], the probability of selecting a pig is [tex]\( 1 \)[/tex] (as the selection is from pigs only).
5. Find the probability of selecting a male pig ( [tex]\( P(\text{Male and Pig}) \)[/tex] ):
Since there are [tex]\( 5 \)[/tex] male pigs and we are only considering pigs, the probability of selecting a male pig is the number of male pigs divided by the total number of pigs.
[tex]\[ P(\text{Male and Pig}) = \frac{5}{10} \][/tex]
6. Calculate the conditional probability [tex]\( P(\text{Male} \mid \text{Pig}) \)[/tex]:
[tex]\[ P(\text{Male} \mid \text{Pig}) = \frac{P(\text{Male and Pig})}{P(\text{Pig})} = \frac{\frac{5}{10}}{1} = \frac{5}{10} = 0.5 \][/tex]
Thus, the probability that an animal is a male, given that it is a pig, is [tex]\( 0.5 \)[/tex] or 50%.
So, the answer for the problem, as per the table data, is:
[tex]\[
\boxed{\frac{5}{10} = 0.5}
\][/tex]
This means there is a 50% chance that a randomly selected animal is a male given that it is a pig.
