A calculator application is being developed.

 According to the ISTQB Tester Foundation Level Agile Tester syllabus, an agile task board is a visual tool that displays the status of the work items in an agile sprint. The task board typically shows the user stories, tasks, and their progress from “to do” to “done”. The task board helps the agile team to monitor and coordinate their work, and to communicate with stakeholders. Therefore, the examples that represent activities that would likely be managed on an agile task board for the third sprint are those that are related to the user stories, tasks, and their progress in the current sprint. Option A is the correct answer, as it contains two examples of such activities: running an acceptance test for a user story, and automating regression tests. These are both tasks that are part of the testing process in the current sprint, and their status can be tracked on the task board. Option B is not a correct answer, as it contains two examples of activities that are not related to the current sprint: designing the features planned for the next sprint, and participating in training in preparation for the fourth sprint. These are both activities that are part of the planning or learning process for the future sprints, and they are not managed on the task board. Option C is also not a correct answer, as it contains two examples of activities that are not related to the current sprint: participating in training in preparation for the fourth sprint, and producing a daily progress report for the agile team members. These are both activities that are part of the learning or reporting process, and they are not managed on the task board. Option D is also not a correct answer, as it contains two examples of activities that are not related to the current sprint: designing the features planned for the next sprint, and producing a daily progress report for the agile team members. These are both activities that are part of the planning or reporting process, and they are not managed on the taskboard. References: ISTQB Tester Foundation Level Agile Tester syllabus, section 2.1.1, page 14; ISTQB Tester Foundation Level Agile Tester syllabus, section 2.1.2, page 15; ISTQB Tester Foundation Level Agile Tester syllabus, section 2.2.1, page 16; ISTQB Tester Foundation Level Agile Tester syllabus, section 2.2.2, page 17.