Answer :
The Solution:
Given that:
Number of cows = 10
Number of pigs = 5
Total number of animals = 15
[tex]\begin{gathered} Pr(\text{Cow)}=\frac{\text{ number of cows}}{\text{ Total number of animals}}=\frac{10}{15} \\ \\ Pr(Pig\text{)}=\frac{\text{ number of pigs}}{\text{ Total number of animals}}=\frac{5}{15} \end{gathered}[/tex]We are required to find the probability of selecting a cow and a pig for testing.
[tex]\begin{gathered} Pr(\text{Cow and Pig)=Pr(Cow and Pig) or Pr(Pig and Cow)} \\ =2\times\text{ Pr(Cow and Pig)}=2\times\frac{10}{15}\times\frac{5}{14}=\frac{10}{3\times7}=\frac{10}{21} \end{gathered}[/tex]Therefore, the correct answer is [option 2]