Full coverage does not define any specific type of coverage, but typically it is used to refer to a car being covered for comprehesive and collision. If state laws do not require you to carry Uninsured/Underinsured Motorist you may not need to keep these coverages depending upon your situation.

If your state requires you to have Uninsured and Underinsured Motorist (UM/UIM)coverages as part of the basic auto insurance policy that complies with the state minimum financial responsibility laws then you will need to carry them on your policy. Even if your state does not require you to carry UM/UIM coverages you may need them depending upon your personal situation. Here is how your current coverages protect you.

Bodily Injury Liability (BI or BIL) coverages cover other people's bodily injuries or death for which you are responsible. Claims for bodily injury may be for such things as medical bills, loss of income or pain and suffering. In the event of a serious accident, you want enough insurance to cover a judgment against you in a lawsuit, without jeopardizing your personal assets. Bodily injury liability covers injury to people, not your vehicle.

Property Damage Liability (PD or PDL) covers you if your car damages someone else's property. Usually it is their car, but it could be a fence, a house or any other property damaged in an accident.

Comprehensive covers your vehicle, and sometimes other vehicles you may be driving for losses resulting from incidents other than collision. For example, comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals.

Collision covers damage to your car when your car hits, or is hit by, another vehicle, or other object. Pays to fix your vehicle less the deductible you choose.

When speaking of Uninsured/Underinsured Motorist this normally refers to Bodily Injury coverage and not Property Damage. Though in some stated both types of UM/UIM coverages are available. If you are talking about UM/UIM Property Damage, than no you would not need this coverage since you would use your Collision coverage if an uninsured motorist hit your vehicle.

However none of the auto insurance coverages that you listed would protect you if you were injured by an uninsured motorist or underinsured motorist.

Uninsured Motorist Bodily Injury coverage pays for medical expenses, lost wages, and other general damages when policyholders, authorized drivers, or passengers are injured in an accident caused by a driver who has no car insurance coverage.
Uninsured motorist coverage may also pay for injuries sustained in hit-and-run accidents depending upon state laws and the terms of your policy.

Underinsured motorist covers you, the insured members of your household and your passengers for injuries, damages or death caused by the negligence of a person with insufficient insurance. If you have an accident with a person whose coverage cannot meet your damages, your policy will meet the difference, up to the limit of liability listed on your policy.

If you have health insurance that you believe you would use if in an accident with an uninsured motorist or underinsured motorist then check with your health insurer since there are some health insurance policies that do not cover these type medical bills. Some medical insurance policies have exclusions for injuries received in auto incidents.

You can check with your medical insurance policy and/or contact their company's representative to find out for certain if your health insurance would cover medical bills related to a car accident and that should help you determine if you need UM and UIM coverages as part of your auto insurance policy.

Your insurance agent can also help you determine if your current coverages meet your needs or if you should add/remove any coverages. If you want to shop around for insurance and make sure you are getting the right insurance for you needs you can use our insurance coverage calculator and then get a quote for low cost car insurance with us.