That’s not the whole story. Consider all of the possibilities of two types of faults, a broken wire and a short circuit.
Let’s say you have an appliance with a metal case, and you have a 2 wire system. The metal case is connected to the neutral wire for safety.
If the hot wire shorts to the case, the breaker trips.
The neutral wire is already shorted to the case, so that’s not a fault.
If the hot wire breaks, the device goes dead, but the case is still grounded and there is no shock hazard. No biggie.
If the neutral wire breaks, and someone turns the device on, the case now becomes “hot” and is a potentially fatal shock hazard.
Now let’s change that to a 3 wire system with a separate safety ground (the green wire) instead of the neutral being used for the safety ground.
If the hot wire shorts to the case, the breaker trips.
If the neutral wire shorts to the case, you technically have a fault, but the case is still grounded so it’s not a shock hazard.
The ground wire is already connected to the case, so the ground wire shorting to the case isn’t a fault.
If the hot wire breaks, the device goes dead, but the case is still grounded and there is no shock hazard.
If the neutral wire breaks, the device goes dead, but the case is still grounded and there is no shock hazard.
If the safety ground breaks, you’ve lost your safety ground, but the device still functions normally, the case doesn’t have any dangerous potential on it, and there is no shock hazard.
So it only takes a particular single fault for the 2 wire system to kill you, but any single fault in a 3 wire system will not kill you. You need to have multiple faults before the 3 wire system becomes potentially deadly (ground wire breaking combined with hot wire shorting to the case, for example).
You wouldn’t. This is the whole reason GFCIs were invented.
A regular breaker protects the wiring. If there is too much current, the breaker will trip. Without the breaker, the wire could overheat and cause a fire that burns down your house (potentially killing you).
But a regular breaker only trips if there is a rather excessive amount of current, more than 15 amps on a typical U.S. circuit. The “safe” level of current that you can pass through the human body is 5 mA, which is 0.005 amps. That’s quite a bit less than 15. So breakers will save you from dying in a fire, but will still easily allow a fatal amount of current to flow through you.
A GFCI (Ground Fault Circuit Interrupter) measures the current through the hot and neutral. If they aren’t the same, then the electricity has found some other path back to ground. It might be through the green wire. It might be through your plumbing. It might be through your home’s aluminum siding. Who knows. But the point is that this is a bad thing. Remember how I said the “safe” current level is 5 mA? Guess what current GFCIs trip at? You guess it, anything greater than 5 mA.
But a regular breaker and a GFCI both won’t protect you from something like a frayed extension cord, which will cause a fire at significantly less than 15 amps. So this is why they created AFCIs (Arc Fault Circuit Interrupters). This protects you from bad extension cords, which historically have been one of the leading causes of house fires.
BTW, “safe” is in quotes throughout this post because it is mostly theoretical with some animal testing to back it up. There hasn’t actually been a whole lot of human testing done to verify this value for reasons that I hope are rather obvious. Most safety standards these days are built around this 5 mA value.
All of this leads to a rather interesting discussion of why do we have a grounded system in the first place? If you keep your electrical system isolated from earth ground, you now have two “hot” wires and you can safely touch either one and not get shocked. You just can’t touch both. And in fact hospital operating rooms and other “wet” locations do use isolated systems, because they are safer (there’s a whole history of how the standard for this evolved out of hospital operating rooms because patients were dying and doctors initially didn’t know why).
So why don’t we use isolated systems for residential power? The reason is that hospitals have to go through great pains to keep their isolated systems isolated, and they have to be tested every year and properly maintained. If you tried to run an entire residential power system completely isolated, what you would find instead is that mother nature would randomly insert ground connections all through your system, by doing things like blowing tree branches into wires and such. It is much easier and safer to have a dedicated safety ground than to have a randomly grounded system. It’s easier to detect ground faults too.
Some ships use isolated systems. Keeping their electrical systems isolated in a salt water environment can take a lot of effort.