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: Find the number of male cattle and total cattle

Number of male cattle \(= 1\).
Total number of cattle \(=1 + 5=6\).

Step2: Use the conditional - probability formula

The formula for conditional probability \(P(B|A)=\frac{P(A\cap B)}{P(A)}\). In the context of frequency (where \(P(A\cap B)\) is the frequency of the intersection and \(P(A)\) is the frequency of \(A\)), for \(P(\text{Male}|\text{Cattle})\), \(P(A\cap B)\) is the number of male cattle and \(P(A)\) is the total number of cattle.
So \(P(\text{Male}|\text{Cattle})=\frac{\text{Number of male cattle}}{\text{Total number of cattle}}\).

Answer:

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