Question

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

Explanation:

Step1: Calculate the total number of sheep

The number of male sheep is \(3\), and the number of female sheep is \(2\). So the total number of sheep \(P(A)=3 + 2=5\)

Step2: Calculate the number of female sheep

The number of female sheep \(P(A\ and\ B) = 2\)

Step3: Use the conditional - probability formula

According to the formula \(P(B|A)=\frac{P(A\ and\ B)}{P(A)}\), substitute \(P(A\ and\ B) = 2\) and \(P(A)=5\) into it. So \(P(\text{Female}|\text{Sheep})=\frac{2}{5}\)

Answer:

\(\frac{2}{5}\)