The FBI is refusing to run nationwide background checks on people applying to run legal marijuana businesses in Washington state, even though it has conducted similar checks in Colorado — a discrepancy that illustrates the quandary the Justice Department faces as it allows the states to experiment with regulating a drug that’s long been illegal under federal law. Washington state has been asking for nearly a year if the FBI would conduct background checks on its applicants, to no avail. The bureau’s refusal raises the possibility that people with troublesome criminal histories could wind up with pot licenses in the state — undermining the department’s own priorities in ensuring that states keep a tight rein on the nascent industry. The Obama administration has said it wants the states to make sure pot revenue doesn’t go to organized crime and that state marijuana industries don’t become a cover for the trafficking of other illegal drugs. At the same time, it might be tough for the FBI to stomach conducting such background checks — essentially helping the states violate federal law. The Justice Department declined to explain why it isn’t conducting the checks in Washington when it has in Colorado.