Virtual function behaviour

Hello experts,

I was just playing around wrote this code.

sundev1:/home/ptiwary/rnd $ cat a1.cpp
#include <iostream>

using namespace std;

class Base
{
    public:
        virtual void foo() { cout << "In Base::foo()" << endl; bar();}
    private:
        void bar() { cout << "In Base::bar()" << endl; }
};

class Der1: public Base
{
    public:
        virtual void foo() { cout << "In Der1::foo()" << endl; bar();}
    private:
        void bar() { cout << "In Der1::bar()" << endl; }
};

class Der2: public Base
{
    public:
        virtual void foo() { cout << "In Der2::foo()" << endl; bar();}
    private:
        void bar() { cout << "In Der2::bar()" << endl; }
};

int main()
{
    Base* b1 = new Base();
    Base* b2 = new Der1();
    Base* b3 = new Der2();

    b1->foo();
    b2->foo();
    b3->foo();

    return 0;
}

sundev1:/home/ptiwary/rnd $ g++ a1.cpp
sundev1:/home/ptiwary/rnd $ ./a.out
In Base::foo()
In Base::bar()
In Der1::foo()
In Der1::bar()
In Der2::foo()
In Der2::bar()

I have 2 questions regarding this.

1. Is the behaviour correct? Because someone told me I need to make
bar() also virtual to get the effect.
2. What is the deal with private virtual functions? Even if I make
bar() virtual, as its private, it won't be accessible from the derived
classes Der1 and Der2 so it does not make any sense having private
virtual functions. Am I right?

Thanks in advance.