Xu and Denison 2009

Chapter 5 endnote 26, from How Emotions are Made: The Secret Life of the Brain by Lisa Feldman Barrett.
Some context is:

...babies can even infer other people’s goals statistically. They can tell the difference when an experimenter chooses a pattern of colored balls randomly versus with intent.

In this experiment, eight-month old babies watched as an experimenter picked five balls from a box of red and white balls, about 80% red and 20% white. In this experiment, the experimenter closed her eyes. The babies expected the experimenter to pick the balls in proportion to the population—four red, one white. We know this because the babies looked longer when the experimenter drew something less probable, (say) one red and four white. Infants spend more time looking at something unexpected (i.e., something they did not predict), usually because it is an opportunity to learn. So this experiment tells us babies can infer simple statistical probabilities based on past experience.

With a slight modification, this type of experiment also shows us that babies can infer other people's goals. In the first phase of the experiment, eleven-month old babies expect the experimenter to retrieve a sample of balls that reflect the proportions in the population (the proportion of red and white balls inside the box), replicating Xu and Garcia (2008). In the second phase of the experiment, the babies were given evidence that the experimenter had a goal to pick only red balls (she picked three red balls from a plexiglass box containing three red balls and three white balls). In the third phase, the experimenter did one of two things: she either put on a blindfold and picked five balls of the same color (either red or white), or she looked into the box and picked out five balls of the same color. When the experimenter could see the balls she was choosing and picked five white balls, babies looked longer than when she picked five red balls, implying that babies were able to ignore the statistical information about which balls were in the box and base their predictions on the experimenter's preferences. When the experimenter was blindfolded, babies ignored her preference because they understood that she could not see the balls she was choosing; their predictions were based on the number of red and white balls in the box.

This experiment demonstrated that babies understood that the experimenter had a goal to pick red balls. When the experimenter could see, the babies were surprised when the experimenter did not meet her goal, and when she was blindfolded, they were surprised when the box’s probabilities were violated. The babies learned not only sensory information about colored balls, and the experimenter’s preference (valence) for a particular color, but also, incredibly, the purely mental goal of the experimenter.