If an insured motorist is at fault and hits an unisured motorist will the insured motorists insurance company pay the expenses of the uninsured person?

Yes, this is because as you stated, the insured driver was at fault. The at fault driver is responsible regardless of the insured status of the person they hit. A good rule of thunb is this,, If they had insurance would I be responsible If the answer is Yes, then the answer is still Yes
Yes, this is because as you stated, the insured driver was at fault. The at fault driver is responsible regardless of the insured status of the person they hit. A good rule of thunb is this,, If they had insurance would I be responsible If the answer is Yes, then the answer is still Yes