Supervisor: Our next budget proposal will probably be approved, because normally about half of all budget proposals that the vice president considers are approved, and our last five budget proposals have all been turned down.
Conclusion
Our next budget proposal will probably be approved.
Evidence (because / and)
Normally about half of all budget proposals that the VP considers are approved, and our last five budget proposals have all been turned down.
Evaluate
Given that ... the VP normally approves about half of these and has turned down the previous five,
How can we argue that ... our next budget proposal won't be approved?
Well, we could maybe say these aren't normal times.
Maybe the VP is in a really weird place with her life / this job right now, and either for strategic or emotional reasons she's going to keep turning stuff down.
Maybe the VP, prior to the last five she turned down, has approved the previous ten (suggesting that if the average rate of approval is 50%, then getting another five proposals rejected could still be in line with that approval rate).
In a sense this is sort of like Gambler's Fallacy -- the idea that . That's not how probability or averages work. The next flip of the coin still is a 50/50 chance.
Goal
The author is assuming that these are normal times, that prior to this streak of rejecting 5 proposals the VP was not on a long streak of approving proposals, that the next budget proposal does not contain some provision the VP hates, that the next proposal is meaningfully different from the previous five, and so forth. It's hard to predict one specific answer here.
The correct answer, when negated, should sound like a big objection to this argument and allow us to argue that, .