1. The problem involves understanding and calculating probabilities given fractions such as $\frac{1}{9}$, $\frac{2}{9}$, $\frac{1}{3}$, and $\frac{4}{9}$.\n\n2. Probability is a measure of how likely an event is to occur, and it ranges from 0 to 1. The sum of probabilities of all possible outcomes must equal 1.\n\n3. The fractions given represent probabilities of different events. For example, $\frac{1}{9}$ means the event has a 1 in 9 chance of occurring.\n\n4. To check if these probabilities are valid and complete, add them: $$\frac{1}{9} + \frac{2}{9} + \frac{1}{3} + \frac{4}{9}.$$\n\n5. Convert $\frac{1}{3}$ to ninths to add easily: $$\frac{1}{3} = \frac{3}{9}.$$\n\n6. Now add all: $$\frac{1}{9} + \frac{2}{9} + \frac{3}{9} + \frac{4}{9} = \frac{1+2+3+4}{9} = \frac{10}{9}.$$\n\n7. Since $\frac{10}{9} > 1$, these probabilities cannot all be correct simultaneously as probabilities must sum to 1 or less.\n\n8. This suggests either an error in the problem or that these fractions represent different, unrelated probabilities rather than parts of a whole.\n\nFinal answer: The sum of the given probabilities is $$\frac{10}{9},$$ which is invalid for a probability distribution because it exceeds 1.