Why would my kitten have diarrhea?

I just bough a siamese kitten from a pet store a week ago today. They told me she's has been de-wormed and her she shot. They also give me a 3lb. bag of Precise kitten food. The day after I got her, she stared to have diarrhea, I've been watching her closely like when she eats and goes to the bathroom. I also have another cat who's 2 years old and Mia my kitten love to seak a few bits of Chanel's food while Chanel eating or when I've forgotten to pick up Chanel's food. Is that why she has diarrhea? Or is it the Precise kitten food? She doesn't act sick, shes always playful.