Chi-Square Distributions and Goodness of Fit

If all four colors were equally likely to be put in the bag, then the expected frequency for a given color would be $1/4\mathrm{th}$ of the lollipops. So, the expected frequency would be $(1 / 4)(40)=10$. (Of course, this is the theoretical expected frequency, not what we actually expect the bag to look like).

Take the sum of each $\text { (expected - observed) }^{2} / \text { expected }=(10-8)^{2} / 10+(10-5)^{2} / 10+(10-12)^{2} / 10+(10-15)^{2} / 10=5.8$