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An animal is randomly selected from this table. What is the probability that it is a male, given that it is cattle?

| | Cattle | Sheep | Chicken | Pig |
|-----------|--------|-------|---------|-----|
| Male | 1 | 3 | 2 | 5 |
| Female | 5 | 2 | 13 | 3 |

[tex]\[
P(\text{Male} \mid \text{Cattle}) = \frac{P(\text{Male and Cattle})}{P(\text{Cattle})}
\][/tex]

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Answer :

GinnyAnswer
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]

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