I am solving some practice questions while revising probabilities and wanted to confirm my methodology. The question is as follows:
A magician has five animals: 2 doves and 3 rabbits- If he pulls 2 animals out at random, what is the chance that he will get a matched pair.
The way I solved it:
Probability of matched pair= Probability of 2 doves (2/5*1/4= 2/20)+ Probability of 2 rabbits (3/5*2/4) = 2/20+ 6/20= 8/20.
But the answer provided is:
Number of ways/ total number of ways= 4/10.
Conceptually both seem appropriate but the answers are different: Is it just that the answer was written as 4/10 instead of 8/20 or can someone please tell me if I am missing something?