DUBLIN, Oct 27 (Reuters) - Ireland has cut its stake in Bank of Ireland, the country’s largest bank by assets, to below 10% for the first time since a state bailout a decade ago, a filing showed on Wednesday. The cut to 9.95% from 10.96% is the fourth sale by the state of shares in the bank since the government announced in June that it planned to sell down part of its 13.9% shareholding before the end of the year. The state had not sold any of its Irish bank share holdings since 2017. Ireland pumped 64 billion euros ($76 billion) or almost 40% of its annual economic output into its banks a decade ago after a property crash, with Bank of Ireland the only lender to avoid majority state ownership. If the government was to maintain its current pace of share sales it could exit Bank of Ireland entirely next year, a move that would make it the first of Ireland’s bailed out banks to fully return to private ownership. (Reporting by Conor Humphries Editing by Mark Potter)