In the trailer, we see Jyn Erso and her small team of rebels looking to put a sting on the Empire and the Death Star, its giant, totally-the-sign-of-reasonable-well-balanced-beings weapon. As they get ready to embark on part of that mission, the droid, K-2SO, helpfully informs the team that there’s “a 97.6 percent chance of failure.” What he doesn’t tell them is where he got the data to calculate those odds.
Is K-2SO a dummy or a liar? Probability is concerned with predicting the likelihood of a certain outcome, but tied up in that outcome are changing variables.
From the trailer, we can assume that the endeavor for which K-2SO is predicting failure is a plot to take on the Empire, meaning that were looking at heavy Empire involvement, and with that involvement comes an assload of variables.
Granted, K-2SO is a reprogrammed Imperial Security Droid; in the best-case scenario, he has some inside knowledge on security measures and protocols, which might be helpful. But we’re probably talking about an attempt to gain access to the Empire. If the Empire’s got a cup’s worth of brains between everyone in its Maniac Base, it would have already controlled for redundancies, changed settings, and prevented bots from tapping into its entire system, especially if those bots can be stolen and reprogrammed.
There’s no way K-2SO has all of the Empire’s info, and even if he did, the element of human variability makes calculating the probability of failure pretty much impossible.
With the assumed context from the trailer, we’re talking about calculating the odds of failure for not a single event, but many events: K-2SO seems to be talking about mission failure, which is going to depend on hundreds of variables — many of which are impossible to foresee — and changing outcomes based on interactions with those variables.
In short, there’s no way that K-2SO could calculate the probability of failure accurately. He’s either a dumb-dumb or he’s lying.