General:
* Arbitrary: This implies a lack of reason or purpose.
* Haphazard: This suggests a lack of order or planning.
* Chance: This emphasizes the role of luck or fate.
* Fortuitous: This implies something happening by chance, especially in a lucky way.
* Unpredictable: This emphasizes the lack of ability to foresee or predict.
* Unplanned: This emphasizes the lack of premeditation.
Specific contexts:
* Data/Sampling:
* Unsystematic
* Unstructured
* Selection:
* Unbiased (if emphasizing fairness)
* Unpremeditated (if emphasizing lack of planning)
* Action/Movement:
* Erratic
* Spontaneous
The best synonym for "random" will depend on the specific context and the nuance you want to convey.