How could Bashir (and Sisko) believe that mutants are correct?

Question

In the Deep Space Nine episode Statistical Probabilities, Bashir works with a group of genetically engineered humans. At some point they all come to the conclusion that

it is 100% sure that Federation will loose the war against the Dominion.

Bashir and the other mutants are so extremely certain that their calculations are correct, that they're willing to risk a lot to prevent this vision from ever happening.

I can understand the other team members, but how could Bashir (and then Sisko) possibly even think that mutants are correct? In Sacrifice of Angels, they were both aboard the Defiant and they saw in the final scene, that

the Prophets can change history with a "snap of their fingers." If they can erase an entire Dominion fleet within a matter of seconds, then it must be obvious to anyone that an entity with such power can do anything they wanted; and that there is absolutely nothing that can be 100% certain in a war theatre, in which this entity is involved.

In other words, if Prophets managed to do what they did in Sacrifice of Angels, then what could prevent them from making Bashir's team "100% certain conclusions" not happen at all?

I like Statistical Probabilities very much, and even find it one of the best episodes in Deep Space Nine; but I'm pretty sure that -- given the above -- their "100% certain conclusions" is based on a completely false assumption.

Can someone confirm that I'm correct, or (if I'm not) can someone tell me where/how I'm wrong?

Answer 1

Sisko

First off, it's worth pointing out that Sisko certainly doesn't accept the group's conclusions that the Federation will lose the war. He finds their work distinctly lacking, largely because they've made assumptions when calculating their probabilities, and that without perfect knowledge of the enemy's disposition, plans and motives, it's impossible to know with total certainty the likely outcome of the conflict.

SISKO: I don't accept it. Your entire argument is based on a series of statistical probabilities and assumptions.

Sisko is very much of the opinion that even faced with insurmountable odds, that freedom is something worth fighting for and hence that their conclusions, no matter how well argued, are basically worthless to him.

SISKO: (emotion rising) Even if I knew what was going to happen with one hundred percent certainty, I still wouldn't ask an entire generation of people to give up their freedom.

Bashir

As a Doctor, Bashir's sensibilities are very heavily aligned with the idea of saving as many lives as possible. As a "mutant" himself he's extremely enamoured of the group's abilities and has a strong emotional investment in proving them right and by extension, proving their (and his own) worth to society.

SISKO: Hang on a minute. How did you come up with all this? Two days ago you said these people were impossible to deal with, now they're turning out projections that would take Starfleet Intelligence months to come up with.

Bashir smiles, shrugs --

BASHIR: We're mutants.

Because of his emotional attachment, he seems willing to overlook the fundamental irrationality of his own argument...

BASHIR: Thank you, sir. (showing him a PADD) The way the statistical model we're using works, the farther into the future we go, the more accurate the projection.

... which neglects (indeed disregards) the fact that small actions can have large consequences and that god-like aliens can turn up at any time.

BASHIR: I understand how you feel, sir. I don't like it any more than you do. But it's the best option. We ran dozens of different scenarios. Even if something unlikely were to happen that tilted the scales in our favor -- say an anti-Dominion coup on Cardassia -- we'd still lose this war.

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In short, both parties are allowing their emotions to cloud their judgment. Sisko is unwilling to even consider surrendering to the Dominion and Bashir is so desperate to prove the Mutants worth that he's willing to overlook the shortcomings of their analysis.