Comparison of olaparib against a placebo in patients with ovarian cancer whose cancer has already improved by taking platinum based chemotherapy. The patients must also have a fault in their DNA which codes for the BRCA protein. The BRCA protein helps mend broken DNA in the cells of the body; if this protein doesn't work properly it can increase the chance of getting cancer. The aim of this study is to see whether patients taking olaparib tablets last longer until their cancer gets worse, compared to those taking the placebo tablet. The study is also looking to see if there is an overall improvement to how long the patients survive whilst taking olaparib tablets compared to the placebo tablets; and the quality of their life whilst living with ovarian cancer.