Making my first beer and during my last temp check I dropped the thermometer into my wort bucket, instinctively i immediately reached in and pulled it out. My hands were cleaned and sanitized and my arm was clean but had not been sanitized. I pitched my yeast and it appears to be fermenting. Did i ruin my batch?
Your beer will probably be fine. Yes, your arm probably left some bacteria in the wort, but the wort is also picking up a few bacteria from the air. Cooled wort has some bacteria and/or wild yeast. But if those numbers are few compared to the number of yeast cells, then the yeast will start eating, creating an environment less friendly to bacteria. The happier you make your yeast, the better chance the yeast will win. I hope you shook the wort for at least one minute to introduce oxygen, since that is one way to make sure your have plenty of happy yeast.