This is a random question If a mother leaves her 11-year-old daughter home alone with her two other children who are 5 and 2 shouldn't the 11-year old have a phone just in case the mother is gone longer than said would be gone?

Yes

Explanation  

You may not trust a 11 year with a phone, but many parents give 11 year old's their own phone. I feel like you should trust them, and they would be responsible enough. I am a 11 year old myself and got my first phone when I was 10. If you don't fully trust them with that privilege buy them a phone that cant have games and can only call and text emergency numbers and your phone number.