Should Each Tenant Carry Renter's Insurance in Multi-Tenant Lease of SFH?

[Chris Troutman]

I entered into a one year lease with 4 tenants (jointly & severally, and collectively referred to as "Tenant"). The Lease requires Tenant to carry a renter’s insurance policy covering Tenant’s household goods, personal property and personal affects in an amount not less than $10,000.00 and liability insurance coverage in an amount of at least $250,000.00 naming Landlord as an Additional Insured. Should I require that each of the 4 tenants obtain such a policy, or would one single policy cover any claims arising from "Tenant's" acts? 

I'm mainly concerned about liability. If Tenant #1 carries the policy, and a guest of Tenant #3 hurts themselves on the property, would the policy apply?