Is it idiomatic to say "I cut myself and blood came out" or "I cut myself and the / my blood came out"?

Question

In this English exercise, they say

The girl had cut herself with a knife and blood was coming out of her thumb.

Why not "her blood was coming out"?

"I cut myself and blood came out" or "I cut myself and the / my blood came out". Right at that moment, you saw the specific blood came out.

Also, Why do native speakers say "I slapped the mosquito and blood came out", which is confusing because we don't know whose blood it is "me or the mosquito"?

Suppose that the mosquito sucked someone's blood and when it was flatten or killed by me, the blood in the mosquito came out, not my own blood. Would we say "I slapped the mosquito and its blood came out"?

Answer 1

You may say

She cut herself, and her blood was coming out of her thumb.

There is nothing ungrammatical in that. It is, however, redundant: how could someone else's blood come out of her thumb. In fact, however, neither sentence is highly idiomatic; what is far more likely is

She cut herself, and her thumb was bleeding.

Your mosquito example is more complex. When I slap a mosquito and find a bloody smear on my arm, I have no idea whose blood it is. So it makes no sense to attach any possesive to the blood.

I slapped a mosquito, and it spurted blood all over my white shirt.

Grammar does not constrain meaning; grammar is the servant of meaning.