Did Yagami Light take a risk while handing over the Death Note to Rem?
People are predictable. Especially if you know one's personality in advance, you can almost accurately predict what one might do with great power, such as the Death Note.

Light is far from stupid, he knew exactly what would happen. He knew he'd use the Death Note to achieve a higher status, and that his and L's team would come and investigate. All a part of clearing their own name.

Basically, Light knew exactly what he was doing. Very little was left to chance in his plan.