a heck load of chemicals injected into a block of soy beans paste.
Everything's a chemical, this is just language used to make things sound scary. The taurin that cats need that isn't found in vegan cat food is identical to the taurin in meat.
Additionally WE can make that choice but cats that are obligatory carnivore would never choose vegan as they are obligated to do so.
If you're so concerned about a cat having a supposedly harmful (the science on this disagrees with you, to be clear) choice made for itself by the human who is keeping it, why are you fine with the choices made for the animals that are kept in awful conditions and then killed for cat food with meat in it? Those animals are also kept by humans and have choices made for them that are unnatural to them, and they are most certainly being harmed.
If a vegan diet is ethical for a cat is unknown.
The science on this is pretty clear, and there are plenty of examples of cats thriving on a vegan diet for many many years. Of course, it's important to consult a specialist and give the cat regular checkups if switching its diet like this.
But in this hypothetical scenario of explicitly unweighted coins, Person A was entirely correct in the odds they gave. There's nothing to improve.