Herd immunity is achieved when a sufficient proportion of a population becomes immune to an infectious disease, either through vaccination or previous infections, thereby providing indirect protection to those who are not immune. The exact percentage needed for herd immunity varies by disease.
In the options you've provided, the first response is the most likely to have reached herd immunity:
40% of the population has been vaccinated; 50% of the population has been exposed to the pathogen.
This scenario suggests that 90% of the population is either vaccinated or has been exposed to the pathogen, which is a good indication of herd immunity being reached, depending on the specific pathogen involved. The other scenarios do not suggest a sufficient level of immunity to achieve herd immunity.