Question

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

Explanation:

Step1: Calculate the number of female animals

Add up the number of female cattle, sheep, chicken and pig: \(5 + 2+13 + 3=23\)

Step2: Calculate the number of female pigs

From the table, the number of female pigs is \(3\)

Step3: Use the conditional - probability formula \(P(B|A)=\frac{P(A\cap B)}{P(A)}\)

Here, \(A\) is the event of being female and \(B\) is the event of being a pig. In the context of frequency (since we are using counts from the table), \(P(\text{Pig}|\text{Female})=\frac{\text{Number of female pigs}}{\text{Number of female animals}}\)
Substitute the values: \(P(\text{Pig}|\text{Female})=\frac{3}{23}\)

Answer:

\(\frac{3}{23}\)