What is the burden of establishing privacy in a search?

"A defendant has the burden at trial of establishing a legitimate expectation of privacy in the place searched or the thing seized. [Citations.] The prosecution has the burden of establishing the reasonableness of a warrantless search. [Citations.] The state may carry its burden of demonstrating the reasonableness of a search by demonstrating that the officer conducting the search had a reasonable belief that the person consenting to the search had authority to do so; it is not required that the state establish that the person consenting to the search had actual authority to consent. [Citations.]." (People v. Jenkins (2000) 22 Cal.4th 900, 972 (Jenkins).)