A purchasing agent must decide to accept or reject an incoming shipment of machine parts. The agent wishes to do either of the following: a1: Accept the shipment a2: Reject the shipment The fraction of defective parts in the shipment is either 0.1 or 0.5 with a prior likelihood of each occurring being 0.5. The costs associated with the possible decisions are €1500 if a 0.1 shipment is rejected and €1000 if a 0.5 shipment is accepted. No costs are incurred if a 0.1 shipment is accepted or a 0.5 shipment is rejected. It is possible to test one part from a shipment as a cost of €10.
(iii) Determine the optimal strategy, that is, what action to take in response to sample outcomes. Show the results of workings on a decision tree.
Decision Tree: 
I'm having trouble getting the third part and I don't know where they go the answer from.
Probability of shipment 1 given test result Ok = where did they get these figures from and how did they do it. 0.17 0.64 0.83 0.36
Hope you can help thank you.
They merely applied the formula that they stated,
$$ P(\theta_j\mid O_k)=\frac{P(\theta_j\cap O_k)}{P(O_k)}\;, $$
which is the standard formula for the conditional probability. For instance, for $j=k=1$,
$$ P(\theta_1\mid O_1)=\frac{P(\theta_1\cap O_1)}{P(O_1)}=\frac{0.05}{0.3}=\frac16\approx0.17\;, $$
where $P(\theta_1\cap O_1)=0.05$ is taken from the previous table and $P(O_1)=0.3$ is stated to the right of that table.