Human adults are adept at mitigating the influence of sensory uncertainty on task performance by integrating sensory cues with learned prior information, in a Bayes-optimal fashion. Previous research has shown that young children and infants are sensitive to environmental regularities, and that the ability to learn and use such regularities is involved in the development of several cognitive abilities. However, it has also been reported that children younger than 8 do not combine simultaneously available sensory cues in a Bayes-optimal fashion. Thus, it remains unclear whether, and by what age, children can combine sensory cues with learned regularities in an adult manner. Here, we examine the performance of 6-7-year old children when tasked with localizing a "hidden" target by combining uncertain sensory information with prior information learned over repeated exposure to the task. We demonstrate that 6-7-year olds learn task-relevant statistics at a rate on-par with adults, and like adults, are capable of integrating learned regularities with sensory information in a statistically efficient manner. We also show that variables such as task complexity can influence young children's behavior to a greater extent than that of adults, leading their behavior to look sub-optimal. Our findings have important implications for how we should interpret failures in young children's ability to carry out sophisticated computations. These "failures" need not be attributed to deficits in the fundamental computational capacity available to children early in development, but rather to ancillary immaturities in general cognitive abilities that mask the operation of these computations in specific situations.