The spell flesh to stone is a powerful way to eliminate a target. However, it calls for multiple saving throws, a complication which makes determining the chance of success or failure challenging. To quote,
You attempt to turn one creature that you can see within range into stone. If the target's body is made of flesh, the creature must make a Constitution saving throw. On a failed save, it is restrained as its flesh begins to harden. On a successful save, the creature isn't affected.
A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration. The successes and failures don't need to be consecutive; keep track of both until the target collects three of a kind.
If I cast flesh to stone on someone and my concentration is not broken, what is the probability that the target is petrified as a function of how likely they are to fail an individual save?
We'll assume that the first failure is included in the tally of three (although you may answer the other case as well if you want).