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About one in 10 Jewish families will need to pidyon haben, when their first baby boy is 31 days old. The qualification is that you need to have a son, delivered naturally (not by caesarian) who is the firstborn of a mother who did not previously have a miscarriage. Neither parent must be the child of a Cohen or a Levi.
The idea behind pidyon haben is that originally the firstborn of each family was dedicated to God for the mission of divine service (Exodus 13:2). But then the people sinned en masse with the Golden Calf. Only the Levites stood firm against temptation. They took over the mantle of divine servants from the firstborns. In memory of this transfer, each firstborn boy is redeemed from the presumption that he will be dedicated to the priestly role.
The ceremony is simple. You first find a Cohen, a priest. The priest asks the father if he would rather have the baby than money. The father says yes, he’d rather have the baby. The father hands over five silver coins to the priests and says two blessings — one for the commandment of pidyon haben and also shehachanu for the privilige of fulfillling the mitzvah. Then you have a party (optional).