Which of the following types of contracts allows the owner to transfer risk to the contractor?

The answer would be E: Fixed Firm Price.

This is on the assumption that the quality of the Project Specifications is suitable to cover any potential deficiencies in the tender design, and that these Project Specifications form part of the Contract.  General terms of the Contract should state that the Contract Price included for all implications required by these Project Specifications.

Without the above being set in place correctly, there is no real transer of risk, as the owner would potentially be exposed to being hit with variations (if these risks came to fruition).  

E. firm fixed price...............

Service contract. The detail needs to be specific with agreed parameters. 

contractor allows the owners Cost plus fixed fee