In the short wait, the children had two consecutive trials; while in the long-wait condition, there was a two-week period between the two trials. Children were given an assortment of red and blue tokens in a ratio of 80:20 and both activated a machine. The chips were placed in the bag and these tipped into the machine. The children were asked which of the chips activated the machine. The results showed that the long wait group guessed which token most accurately reflected the proportion of red tokens to blue tokens. This confirms that independence between samples is necessary for accurate probability matching. Next, this experiment was extended to test the theory of noisy maximization. The children were presented with three different “conditions”: a 95:5 condition, a 75:25 condition, and a 50:50 condition. If noisy maximization theory were true, children would have the same response for the 95:5 condition and the 75:25 condition. Indeed, in both conditions, children process at ceiling levels which, in this case, are set at approximately 72%. The results show that children's guess about the red token had a linear relationship with the proportion of the red token to the blue token. This showed that children did not actually use this strategy to solve causality problems, leaving room for naive frequency matching and sampling assumptions. The third experiment was the same as the second, but with three conditions instead of two. The children therefore had three possible hypotheses with different probabilities. The results showed that children's response can still be predicted via the sampling hypothesis when multiple choices exist. The final experiment tested whether children used a sampling hypothesis or naive frequency matching. The children were given two bags, one had a red-to-blue ratio of 14:6 and the second bag had a red-to-blue ratio.