To determine the probability that an animal is male given that it is cattle, we need to use the conditional probability formula, which is given by:
[tex]\[ P(\text{Male} \mid \text{Cattle}) = \frac{P(\text{Male and Cattle})}{P(\text{Cattle})} \][/tex]
Let's break down the steps involved in computing this probability.
1. Determine the number of male cattle:
According to the table, there is 1 male cattle.
2. Determine the number of female cattle:
According to the table, there are 5 female cattle.
3. Calculate the total number of cattle:
[tex]\[ \text{Total number of cattle} = \text{Number of male cattle} + \text{Number of female cattle} = 1 + 5 = 6 \][/tex]
4. Calculate the probability that an animal is male given that it is cattle:
[tex]\[ P(\text{Male} \mid \text{Cattle}) = \frac{\text{Number of male cattle}}{\text{Total number of cattle}} = \frac{1}{6} \][/tex]
So, the probability that an animal is male, given that it is cattle, is [tex]\(\frac{1}{6}\)[/tex].
To conclude:
- Number of male cattle: 1
- Number of female cattle: 5
- Total number of cattle: 6
- Probability that an animal is male given that it is cattle: [tex]\(\frac{1}{6} \approx 0.167\)[/tex]
