MathNet 2002 — Part 01 Question 146

Question 146

In a map of a certain region there are ten cities at the vertices of a regular decagon, and the ten sides of the decagon represent as many roads. There is construction in the region, so each road is open with a probability of $\frac{1}{2}$ regardless of the others.
What is the probability that every other city can be reached from every city?

between $0,2 \%$ and $0,5 \%$
between $5 \%$ and $10 \%$.
between $0,5 \%$ and $1 \%$
between $1 \%$ and $2 \%$
between $2 \%$ and $5 \%$