To add to PTGuy's comment, the equation works like this:
Premium = Expected Claims + Commission to Sales Person + Commission to Dealer + Profit Margin + Risk Margin + Admin Expenses.
In the extended warranty business, the Premium is significantly higher than the expected claims. The underwriter has lots of figures to gauge expected claims.
Yes, a minority of buyers, it will turn out to save them money. But the odds are you would rather be the insurer than the insured in that equation. This "peace of mind" that the dealers talk about is just a very expensive way of prepaying for repairs. So just set the money aside and be the insurer. You will come out ahead mnay thousands over your lifetime if you never buy an extended warranty.
Now this equation holds to some extent for all "insurance". But true insurance is for low probability, but high impact things like fire insurance, liability insurance, life insurance, etc... For these if you have a claim it will be thousands times your premium. And for these types of insurance, the commissions and margins are not as large.. So buying insurance makes sense as you can't self insurer a catastrophic claim. But for extended warranties, what's the worst case scenario? maybe a claim of 4x to 5x the premium at the worst (very rare). these things, it makes sense to self insure and keep funds aside to pay for repairs. The other consideration is if a car model has some really major issues, manufacturers may extend the base warranty to address complaints.
Also you're buying a Mazda, a brand with very high reliability scores. Buy reliable brands, have money set aside, and self-insure.