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The 91-year-old Briton, now in Portugal, said a "silly, tiny little incident" had caused a lot of aggravation as he and his family tried to leave Sao Paulo by private plane on Wednesday night.
Ecclestone acknowledged owning the gun, but said he was unaware it was in his luggage at the time, police said.
Ecclestone said that not only was his wife happy, but also he didn't understand what the fuss was all about.
Ecclestone's wife Fabiana Flosi, 44, has given birth to a baby boy and he has been named Ace.
Former Formula One supremo Ecclestone had earlier told CNN in an interview that 'in lots of cases, Black people are more racist than what white people are.'
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