As RIP and OSPF are both different routing protocol and their behaviour is also different. By default, both will not share any such kind of information with each other.
There is a mechanism which is called redistribution will use for import one routing protocol's routes into another protocol as an import from OSPF and Export into RIP. But keep in mind that this is not an actual import and export between routing protocols. It will share only those routes which are installed in the routing table by the router where you did redistribution. This may one way or both ways means OSPF to RIP or OSPF to RP and RIP to OSPF.
During the redistribution, the importer routing protocol will assign some short of COST/Metric and it completely depends on the importer routing protocol.
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