In the short wait the children did two consecutive tests; while in the long wait condition there was a period of two weeks between the two tests. The children were presented with an assortment of red and blue tokens in an 80:20 ratio and both activated a machine. The chips were placed in the bag and it tipped over in the machine. The children were asked which of the chips activated the machine. The results showed that the group in the long wait condition guessed which chip most closely reflected the ratio of red chips to blue chips. This supports the need for independence between samples for accurate probability matching. This experiment was later expanded to test the noisy maximization theory. 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 as for the 75:25 condition. This is because in both conditions children process at maximum levels which in this case are set to a value of approximately 72%. The results show that children's guess about the red chip had a linear relationship with the proportion of the red chip to the blue chip. This demonstrated that the children did not actually use this strategy to solve causality problems, leaving naïve frequency matching and sampling assumptions. The third experiment was the same as the second only with three conditions instead of two. So the children had three possible hypotheses with different probabilities. The results showed that children's response can still be predicted via the sampling hypothesis when there are multiple choices. The final experiment tested whether children use naïve sampling or frequency matching assumptions. The children were presented with two envelopes: one had a red-blue ratio of 14:6 and the second bag had a red-blue