Voltage in circuit (beginner)
The voltage across a resistor is given by Ohm's Law:

$$V = I R$$

In this case, one end of the resistor is an open circuit (it's not connected to anything else). Therefore the current through the resistor is 0 A.

$$0\ \mathrm{A}\times 15\ k\Omega = 0\ \mathrm{V}$$

So the voltage drop across the resistor is 0.

The voltage across a series combination of two elements is the sum of the voltages across the individual elements:
$$2\ \mathrm{V} + 0\ \mathrm{V} = 2\ \mathrm{V}$$

Therefore the voltage \$V_O\$ is 2 V.

If you were to connect any load at all to the output terminals, allowing some current to flow, then your analysis would be correct and the output voltage would drop below 2 V.