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Exsanguination (or bleeding out) is the main cause of death when you are losing blood fast.
The average human adult I think, has approximately 8 pints of blood in their body at any given time, if not bleeding. This includes both blood that is oxygenated and not oxygenated. To lose 4 pints of blood would be a serious injury. Indeed, it would be VERY difficult to survive losing that amount, as that is basically losing around 85% of your total blood volume.
Here are some statistics to help. There are 4 stages of Hypovolemic Shock, which results from not blood, but specifically blood plasma, which is the liquid part of blood. By stage 3, you have lost probably around 35% of your blood volume. In this case, it is POSSIBLE that you may live with immediate transplant or treatment. beyond that is a stage 4 Hypovolemic Shock, which is around 45 to 50 percent of your blood volume gone. By this stage, you will be so far in shock that you may not even realize you are dying. This stage is extremely FATAL. Sadly, most patients die in this stage, due to organ failure as your body begins to shut down.
So, given that scale, if you lose around 45 to 50 percent of your blood, which is around....3.5 pints or so......you are most likely going to die.
So, to answer your question, losing 4 pints of blood is fatal, yes.
The above is mostly accurate, I just want to clarify a few things. First, the average male has 10-12 pints of blood, on average, while the average female has 8-10. I usually quote a general average as 10.
Second, the above has a math error when stating that losing 4/8 pints was 85% the total blood volume... I'm not sure where that came from. That's actually 50% by your quoted values, and closer to 40% by the actual values. This aligns much better with fourth stage hypovolemic shock.
By these points, the above answer, that losing 4 pints of blood is fatal, is totally accurate. But you have to take into account a few other things. How fast are they losing blood? How quickly did they get medical attention? Et cetera. Blood volume itself is a key factor, which is why in an emergency a saline infusion will be given to increase blood volume. If blood loss is relatively gradual and medical attention relatively immediate, a person in good health can survive losing much more than four pints of blood. Exsanguination occurs mainly from rapid blood loss.