Inclusion Criteria:  Capable of giving signed informed consent, which includes compliance with the requirements and restrictions listed in the informed consent form and in the study protocol. Provision of signed and dated, written informed consent form prior to any mandatory study specific procedures, sampling, and analyses.  For inclusion in i) the optional exploratory genetic research and ii) the optional biomarker research, patients must fulfill the following criteria:  Provision of informed consent for genetic research prior to collection of sample. Provision of informed consent for biomarker research prior to collection of sample.  If a patient declines to participate in the optional exploratory genetic research or the optional biomarker research, there will be no penalty or loss of benefit to the patient. The patient will not be excluded from other aspects of the study.  Patients must be ≥18 years of age (or ≥19 years of age in South Korea) at the time of signing the informed consent form. For patients enrolled in Japan who are <20 years of age, written informed consent should be obtained from the patient and from his legally acceptable representative. Histologically or cytologically confirmed prostate adenocarcinoma. Metastatic status defined as at least 1 documented metastatic lesion on either a bone scan or a computed tomography(CT)/ magnetic resonance imaging (MRI) scan. First-line metastatic castration-resistant prostate cancer (mCRPC). Ongoing androgen deprivation with gonadotropin-releasing hormone analogue or bilateral orchiectomy, with serum testosterone <50 nanograms per decilitre (ng/dL) (<2.0 nanomoles per litre (nmol/L)) within 28 days before randomisation. Patients receiving androgen deprivation therapy (ADT) at study entry should continue to do so throughout the study. Candidate for abiraterone therapy with documented evidence of progressive disease. Patients must have normal organ and bone marrow function measured within 28 days prior to administration of study treatment. Eastern Cooperative Oncology Group (ECOG) performance status 0-1, with no deterioration over the previous 2 weeks. The participant has, in the opinion of the investigator, a life expectancy of at least 6 months. Prior to randomisation, sites must confirm availability of either an archival formalin fixed, paraffin embedded (FFPE) tumour tissue sample, or a new biopsy taken during the screening window, which meets the minimum pathology and sample requirements in order to enable homologous recombination repair (HRR) status subgroup analysis of the primary endpoint radiographic progression-free survival (rPFS). If there is not written confirmation of the availability of tumour tissue prior to randomisation, the patient is not eligible for the study. Male patients must use a condom during treatment and for 3 months after the last dose of olaparib+abiraterone when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential.  Exclusion Criteria:  Has a known additional malignancy that has had progression or has required active treatment in the last 5 years. Patients with myelodysplastic syndrome (MDS)/ acute myeloid leukaemia (AML) or with features suggestive of yelodysplastic syndrome (MDS)/ acute myeloid leukaemia (AML). Clinically significant cardiovascular disease Association Class II-IV heart failure or cardiac ejection fraction measurement of <50% during screening as assessed by echocardiography or multigated acquisition scan. Planned or scheduled cardiac surgery or percutaneous coronary intervention procedure. Prior revascularisation procedure (significant coronary, carotid, or peripheral artery stenosis). Uncontrolled hypertension (systolic blood pressure (BP) ≥160 millimeters of mercury (mmHg) or diastolic blood pressure (BP) ≥95 millimeters of mercury (mmHg)). History of uncontrolled pituitary or adrenal dysfunction. Active infection or other medical condition that would make prednisone/prednisolone use contraindicated. Any chronic medical condition requiring a systemic dose of corticosteroid >10 milligrams (mg) prednisone/prednisolone per day. Patients who are considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Persistent toxicities (Common Terminology Criteria for Adverse Events [CTCAEs] grade >2) caused by previous cancer therapy, excluding alopecia. Patients with brain metastases. A scan to confirm the absence of brain metastases is not required. Patients with spinal cord compression are excluded unless they are considered to have received definitive treatment for this and have evidence of clinically stable disease for 4 weeks. Patients who are unevaluable for both bone and soft tissue progression Patients who are unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. Immunocompromised patients Patients with known active hepatitis infection (ie, hepatitis B or C). Any previous treatment with Polyadenosine 5'diphosphoribose [poly (ADP ribose)] polymerase (PARP) inhibitor, including olaparib. Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment. Patients who receive palliative radiotherapy need to stop radiotherapy 1 week before randomisation. Any previous exposure to a Cytochrome P450 (CYP) 17 (17α-hydroxylase/C17,20-lyase) inhibitor (eg, abiraterone, orteronel). Concomitant use of known strong Cytochrome P450 (CYP) 3A inhibitors (eg, itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg, ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting study treatment is 2 weeks. Concomitant use of known strong Cytochrome P450 (CYP) 3A inducers (eg, phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine or St John's wort) or moderate Cytochrome P450 (CYP) 3A inducers (eg, bosentan, efavirenz or modafinil). The required period prior to starting study treatment is 5 weeks for phenobarbital and enzalutamide and 3 weeks for other agents. Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery. Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT). Participation in another clinical study with an investigational product or investigational medical devices within 1 month of randomisation. History of hypersensitivity to olaparib or abiraterone, any of the excipients of olaparib or abiraterone, or drugs with a similar chemical structure or class to olaparib or abiraterone. Involvement in the planning and/or conduct of the study (applies to both AstraZeneca and Merck staff and/or staff at the study site). Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements. Previous randomisation in the present study.