Final answer:
The album by The Police that is based on Carl Jung's psychological writings is 'Synchronicity.' This 1983 album delves into themes related to synchronicity and other aspects of Jung's work. Therefore, the correct option is a) synchronicity.
Step-by-step explanation:
The Police album that is based on the psychological writings of Carl Jung is Synchronicity. This 1983 release is the band's fifth and final studio album. It explores themes of Jung's philosophy, including the concept of synchronicity, which is an idea that events are "meaningful coincidences" if they occur with no causal relationship yet seem to be meaningfully related.
Synchronicity was a major commercial success and includes hits like 'Every Breath You Take' and 'King of Pain.' The album's inspiration from Jung's writings is especially evident in the title track, where lyrics reference some of his theories and ideas.