To determine the probability that an animal is male given that it is cattle, we need to follow these steps:
1. Identify the numbers of male and female cattle from the table:
- Male Cattle: 1
- Female Cattle: 5
2. Calculate the total number of cattle:
To find the total number of cattle, we sum the number of male and female cattle.
[tex]\[
\text{Total Cattle} = \text{Male Cattle} + \text{Female Cattle} = 1 + 5 = 6
\][/tex]
3. Calculate the probability that an animal is male given that it is cattle:
The probability of an event [tex]\( A \)[/tex] given [tex]\( B \)[/tex] is defined as:
[tex]\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\][/tex]
In our specific example, [tex]\( A \)[/tex] is the event that the animal is male, and [tex]\( B \)[/tex] is the event that the animal is cattle. The intersection of these events [tex]\( A \cap B \)[/tex] is simply the event that the animal is a male cattle.
Therefore, the probability that an animal is male given that it is cattle is calculated as follows:
[tex]\[
P(\text{Male}|\text{Cattle}) = \frac{\text{Number of Male Cattle}}{\text{Total Number of Cattle}} = \frac{1}{6}
\][/tex]
Hence, the probability that an animal is male given that it is cattle, [tex]\( P(\text{Male}|\text{Cattle}) \)[/tex], is:
[tex]\[
\boxed{0.16666666666666666} \approx 0.167
\][/tex]
