Are toddlers supposed to care when their siblings hurt themselves?

Empathy SHOULD happen by 2 years of age so if a 3 year old seems not to have it, talk to the doctor

Toddlers around 8 to 10 years old SHOULD care , yes !

Depends on the kid, really. Both of mine developed strong senses of empathy pretty early, my younger one especially. She's about to turn 3 but she is incredibly emotionally savvy for such a little kid. Other kids don't really have the ability to model the experiences of others in their minds until they're a little older, and that's perfectly normal. As long as the 3 year old isn't actually hurting the baby, you don't necessarily have anything to worry about.

Normal.  A 3-year old only thinks of themselves and could care less about anyone else.  Perhaps you should put your baby in a walker.

Toddlers rarely show empathy for anyone. They are in their own world and often don't understand things like danger and other people being hurt. Doesn't mean your child will grow up with no compassion or hates thier sibling, it just means they're young. Perfectly normal don't worry

yes that is perfectly normal for a really young kid

kids that age believe the world revolves around them and dont have any empathy for anyone else

Yes it's normal, i'm sure.  

It's not uncommon for someone that young to not understand what's going on and/or not display empathy.

The 3 y/o is probably just busy doing their own thing and is totally accustomed to the baby crying anyway.

They'd likely be more upset based upon your cues; if you were upset, they would be more worried.

that dont sound normal to me

Yeah, pretty much normal. Most kids that age are not really in touch with empathy, some will be upset by it, but generally, if the issue doesn't directly relate to the older sib, they won't really worry about it. Now would be a good time to start showing what empathy is, so that they will learn.