Do most woman have ovarian cysts at some time in there life?

Yes. The simple answer is yes. The more complex answer is that the significance of cysts varies widely based their size, structure, timing with regard to period and to menopause, etc. I will share this with subspecialists in reproductive endo and onc for additional input.
Yes, but... All women with working ovaries have natural cysts in their reproductive lifetime. Ovulation involves a cyst (a follicle, ) Progesterone production and early pregnancy needs a cyst (corpus luteum, ) and there are others. Cyst is a generic term referring to a fluid-fileld sac anywhere in a body. A challenge for gynecologists can be sorting out which ovarian cysts are normal and which not.