What are the chances of getting a frozen carrot from a Bonny Bunny?

Question

After using a soft hammer on a Bonny Bunny, you can get 1 of 2 messages.

"As soon as you reach out for the stunned rabbit it comes to its senses and flees. It seems to have left something" which will leave a frozen carrot.

"As soon as you reach out for the stunned rabbit it comes to its senses and flees" which leaves you with nothing.

What are the chances of successfully obtaining a frozen carrot?

Answer 1

It is not 100% but it is high, because I have farmed the item and practically all the rabbits have given me carrots. I kill 30 and I get 26 carrots.

Answer 2

After hitting 100 Bonny Bunnies, 11/100 did not produce a carrot so the failure rate for me was 11%