Circular Regions

Four random points $P_1, P_2, P_3$ , and $P_4$ are chosen on the circumference of a circle. A chord is drawn between $P_1$ and $P_2$ , and another chord is drawn between $P_3$ and $P_4$ . What is the expected number of separate regions into which the circle is divided?

Enter your answer rounded to 5 decimal places.