Question

an animal is randomly selected from this table. what is the probability that it is a male, given that it is cattle?
animals on a farm
cattle sheep chicken pig
male 1 3 2 5
female 5 2 13 3
p(male | cattle) =
p(b|a) = \frac{p(a and b)}{p(a)}

Explanation:

Step1: Calculate the total number of cattle

The number of male cattle is \(1\) and the number of female cattle is \(5\). So the total number of cattle \(n(\text{cattle})=1 + 5=6\)

Step2: Calculate the number of male cattle

The number of male cattle \(n(\text{male and cattle}) = 1\)

Step3: Use the conditional - probability formula

The formula for conditional probability \(P(B|A)=\frac{P(A\cap B)}{P(A)}\). In the case of frequency (counts), if \(A\) is the event "cattle" and \(B\) is the event "male", then \(P(\text{Male}|\text{Cattle})=\frac{n(\text{male and cattle})}{n(\text{cattle})}\)
Substitute \(n(\text{male and cattle}) = 1\) and \(n(\text{cattle})=6\) into the formula: \(P(\text{Male}|\text{Cattle})=\frac{1}{6}\)

Answer:

\(\frac{1}{6}\)