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 cattle 1 sheep 3 chicken 2 pig 5 female 5 2 13 3 p(pig | female) = ? p(b|a) = \frac{p(a and b)}{p(a)}

Explanation:

Step1: Find P(A and B)

The number of female pigs is 3. The total number of animals is \(1 + 3+2 + 5+5 + 2+13 + 3=34\). So \(P(\text{Pig and Female})=\frac{3}{34}\).

Step2: Find P(A)

The number of female animals is \(5 + 2+13 + 3 = 23\). So \(P(\text{Female})=\frac{23}{34}\).

Step3: Calculate P(Pig|Female)

Using the formula \(P(B|A)=\frac{P(A\text{ and }B)}{P(A)}\), we substitute the values: \(P(\text{Pig}|\text{Female})=\frac{\frac{3}{34}}{\frac{23}{34}}=\frac{3}{23}\).

Answer:

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