Bill and Brenda are considering changing from their current HMO to a PPO with a $80/20$ coinsurance provision in$-$network, a $60/40$ coinsurance provision out$-$of$-$network, and annual deductibles of $$250$ per person and $$500$ for the family. Preventive care is covered at no charge and hospital stays are covered $.$ You are the HR representative and Bill asks you to explain to him how coverage for expenses will be different.

Identify and briefly describe the major differences between HMOs and PPOs to Bill and Brenda.

For one of the events above, mathematically explain to Bill how the payment for the services would be different $($specifically$,$ how much would the PPO pay in comparison to the HMO$)?$