How does the ternary operator evaluate the resulting datatype?

Given this piece of code

public class Main {

    public static void main(String[] args) {
        foo(1);
        foo("1");
        foo(true?1:"1");
        foo(false?1:"1");
    }

    static void foo(int i){System.out.println("int");}
    static void foo(String s){System.out.println("String");}
    static void foo(Object o){System.out.println("Object");}
}

This is the output I get:

int
String
Object
Object

I can't understand why in the last two cases foo(Object o) is invoked, instead of foo(int i) and foo(String s). Isn't the return type for a ternary expression evaluated at runtime?

Edit:

What was confusing me is the assertion that

System.out.println((y>5) ? 21 : "Zebra");

compiles because (OCA Study Guide - Sybex):

The System.out.println() does not care that the statements are completely differnt types, because it can convert both to String

while the point is that println is overloaded to accept Object types as input. Quite misleading, imho.