What is the purpose of PMI (private mortgage insurance)?

I have a question. All conventional mortgages when the buyer has reduced to less than 20% deposit is required to buy PMI (private mortgage insurance) which is to “protect” the lender against loss if the borrower defaults. When an FHA loan, they are insured by the federal government. Given this, why not instituitions ready to collect their losses from insurance companies? Does the government does not support the FHA loan? Please help me understand why, but now buyers need PMI, lenders require that we help?

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