Formula One said in a statement on Thursday that the foundation would finance primarily internships and apprenticeships for under-represented groups.
"We fully recognise that Formula One needs to be more inclusive and diverse. While we set out our strategy last year to improve the position of our sport, we need, and want, to do more," said Carey.
"That is why we will establish a Task Force to listen and ensure the right initiatives are identified to increase diversity in Formula One.
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"We want to ensure we give people from all backgrounds the best chances to work in Formula One regardless of their gender, ethnicity, sexual orientation, or physical abilities."
The plan, in partnership with the governing FIA, also aims to promote driver diversity by "identifying and systematically eliminating" barriers to entry.

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Six times world champion Lewis Hamilton, the sport's first black champion whose paternal grandparents came to Britain from the Caribbean, has been critical of the lack of diversity around him.
The Briton has also called out his sport's initial silence over the killing of George Floyd, an unarmed Black man who died in Minneapolis after a white U.S. police officer knelt on his neck last month.
The Mercedes driver last week announced his own commission to help motorsport engage more young people from Black backgrounds.
"When I look back in 20 years, I want to see the sport that gave a shy, working-class black kid from Stevenage so much opportunity, become as diverse as the complex and multicultural world we live in," the Briton said then.
Formula One, owned by U.S.-based Liberty Media, announced a diversity and equality task force on Monday.
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