Which one of the following is the coolest star?

The color of a star is determined by its surface temperature. Cooler stars have lower surface temperatures, while hotter stars have higher surface temperatures.

Blue color stars are generally the hottest, followed by yellow-white color stars. These stars have high surface temperatures and emit a large amount of blue and white light.

Red color stars, on the other hand, have lower surface temperatures compared to blue and yellow-white stars. They emit more red light and less blue or white light. This gives them a reddish appearance.

Purple color stars are not commonly found in nature. The colors of stars are primarily determined by their surface temperatures, and purple is not a typical color associated with stars. 

Therefore, the option "coolest star would be the red color star" is correct.