There has to be a formula!

O is the observed frequency. This comes from the data.

E is the expected frequency. This is based on the percentages you have hypothesized.

How do we find the expected frequency?
Multiply the expected proportion by the total number of cases. For our discrimination example, the hypothesized proportion is .50. For 10 cases, .50 x 10 = 5. For 100 cases, .50 x 100 = 50. If you calculated this value for our 10 people example, it would .4.