There is a group of people, each individual with probability $0.2$ has $0$ child, with probability $0.6$ has $1$ child, with $0.2$ has $2$ children, then after a very long(you can think as infinity long) time
A This group will be extinct
B This group will have a population of infinity
C The population of this group will be stable in a range
D Not enough information
Intuitively, Because Expectation=$0.2*0+0.6*1+0.2*0.2=1$, so I feel it should be stable in a range. But why this is wrong?
I want to get a feeling why it will be extinct? Or how can we explain it intuitively?