In this example, there are G = 6 groups (cells). Assuming the die is fair, the probability that a roll results in a 1 is p1 = 1/ 6, the probability that a roll results in a 2 is p2 = 1 / 6, etc. In goodness-of-fit tests, the expected values are found from some hypothesized distribution that determines the probability for each of the G groups.
In this case, we assume p1 = p2 = p3 = p4 = p5 = p6 = 1 / 6. The expected count for each of the 6 groups can be found from n × pi. Assuming all outcomes are equally likely, fill out the expected counts in Table 6.8.
Table 6.8 Observed and expected results of 30 rolls of a die.

2 4 Observed2 Expected