Apple Inc. has made a lot of daring bets over the years. Now the maker of the iPhone is gambling that millions of American consumers can do a little simple math.

Apple has struck deals with the cellphone carriers Virgin Mobile and Cricket Wireless to offer the iPhone 4 and 4S on a no-contract basis. Instead of being locked into 24 monthly payments, customers will pay month to month and can drop the service whenever they choose, with no financial penalty.