Simply because it is a binary choice and infinity is equal to infinity, in this case, since we are using whole numbers. To try to state it another way, you cant have more infinity of [object 1], than infinity of [object 2], if those are your only two options.
No, that's not how it works. Infinity is not equal to infinity, it's not a number, you can't do arithmetic on it.
Consider that your argument applies to anything, leading to nonsensical results like 'Mark either spontaneously turns into a duck or he doesn't, it's a binary choice, both are infinite therefore both outcomes are equally likely'