A local bank reports that 80% of its customers maintain a checking
account, 60% have a savings account, and 50% have both. If a customer
is chosen at random, what is the probability the customer has either a
checking or savings account? What is the probability the customer does
not have either a checking or savings account?

This smells like homework. 

aNoNiM

Is it possible for a bank customer to have neither a checking nor a
savings account?  That will affect the answer.