To complete a tree diagram with probabilities we just need that each branch adds up to 1. For example in the upper branch we have:
[tex]\begin{gathered} \frac{1}{10}+x=1 \\ x=1-\frac{1}{10} \\ x=\frac{9}{10} \end{gathered}[/tex]
Then we need to fill the W-OT line with a 9/10.
Similarly for the lower branch we have:
[tex]\begin{gathered} y+\frac{19}{20}=1 \\ y=1-\frac{19}{20} \\ y=\frac{1}{20} \end{gathered}[/tex]
Then we need to fill the B-L line with 1/20.
Finally the first empty line we have:
[tex]\begin{gathered} z+\frac{1}{3}=1 \\ z=1-\frac{1}{3} \\ z=\frac{2}{3} \end{gathered}[/tex]
Then the first empty slot is 2/3
