It happened Tuesday afternoon in the boys' home in the 7000 block of South Yale.
Damion Rolle was rushed to a hospital where he later died. Police took his older brother from the scene.
The boys' big sister, who was at home at the time of the shooting, is sure it was an accident.
"There was no argument, no nothing, I just heard them talking," said Shatoya Hubbard, Rolle's sister. "And I just heard a 'bow' and then he said you shot me. That's when I went in and Damion, my little brother, was lying on the floor and I was asking him what happened, I kept asking him what happened."
Family members say the brother accused of shooting Rolle is autistic.