I have been working a lot on constructing Dutch books today - and it seems that the notes makes things far more long-winded than needed.
Could someone check through my answer for the mock exam and see if it makes sense?
We are given A ⊂ B, but flat mate believes P(A) > P(B). Want to construct a dutch book against them.
For n large enough, there is r_1, r_2 such that P(A) = r_1/n, P(B) = r_2/n.
The flat mate's probabilities suggest that they believe there is a positive k such that r_1 = r_2 + k.
Make a bag of n balls with r_2 red, k green, rest black.
Then b(B) ~ b(n,r_2) - drawing a red, b(A) ~ b(n, r_2 + k), red or green.
Suppose the flat mate holds b(B). Then they are happy to swap for b(n,r_2). They are then happy to pay a small amount £c for b(n,r_2 + k), which he is happy to swap back for b(A). But since A ⊂ B, the flat mate pays £c for a bet on something less likely!