This interesting work (PDF here) shows that 12 month old infants have expectations about future single events never before seen, based on their likelihood. The authors presented movies in which three identical objects and one different in color and shape bounced randomly inside a container with an open pipe at its base, as in a lottery game. After 13 s, an occluder hid the container and one object, either one of the three identical objects (probable outcome) or else the different one (improbable outcome), exited from the pipe. The infants looked significantly longer when they witnessed the improbable outcome.
The authors also show that it only after ~3 years of age that children can overrule their probabilistic intuition when an experienced frequency of outcome disagrees with prior probability.
The article's introduction (slightly edited) sets the context for the work:
Rational agents should integrate probabilities in their predictions about uncertain future events. However, whether humans can do this, and if so, how this ability originates, are controversial issues. One influential view is that human probabilistic reasoning is severely defective, being affected by heuristics and biases. Another influential view claims that humans are unable to predict future events correctly without experiencing the frequency of past outcomes. Indeed, according to this view, in the environment in which we evolved only "the encountered frequencies of actual events" were available, hence predicting the probability of an event never before observed is meaningless.
A third, largely unexplored view is that intuitions about possible future events ground elementary probabilistic reasoning. Against this view, several classic, although not unchallenged, studies seemingly show that probabilistic reasoning appears late in development and requires frequency information. However, if, as Laplace wrote, probability theory "makes us appreciate with exactitude that which exact minds feel by a sort of instinct", humans must have intuitions about probabilities early in their life. The present work supports this view.