Previous research has revealed that infants can reason correctly about single-event probabilities with small but not large set sizes (Bonatti, 2008; Teglas "et al.", 2007). The current study asks whether infants can make predictions regarding single-event probability with large set sizes using a novel procedure. Infants completed two trials: A preference trial to determine whether they preferred pink or black lollipops and a test trial where infants saw two jars, one containing mostly pink lollipops and another containing mostly black lollipops. The experimenter removed one occluded lollipop from each jar and placed them in two separate opaque cups. Seventy-eight percent of infants searched in the cup that contained a lollipop from the jar with a higher proportion of their preferred color object, significantly better than chance. Thus infants can reason about single-event probabilities with large set sizes in a choice paradigm, and contrary to most findings in the infant literature, the prediction task used here appears a more sensitive measure than the standard looking-time task.