The correct answer is 'Canary deployments,' because this strategy allows for slowly rolling out the change to a subset of users before making it available to everybody. This approach is particularly useful for minimizing the impact on the production environment if a rollback is necessary due to unforeseen issues with the new version. A 'Blue/green deployment' is incorrect because it involves two separate but identical environments where traffic is switched all at once, not gradually. 'Rolling deployments' is also incorrect as it gradually replaces instances of the old version with the new one on a rolling basis without specifically targeting a population percentage. Lastly, 'All-at-once deployments' is incorrect since it deploys the new version to all instances simultaneously, which would not allow for the controlled exposure or easy rollback that the scenario requires.