Answer to Question #25490 in Statistics and Probability for Julia

Question

Dear math experts, I have a problem with my probability homework... The question is the following: "A pencil-and-paper betting game can be played. Draw six vertical lines on a sheet of paper. The first player joins pairs at the upper ends in any manner, the folds back the top of the paper to conceal the connecting lines from his opponent. The second player now joins pairs of bottom ends as shown at the left in the figure below. The sheet is unfolded to see if the second player has won by forming one large closed loop. Whom does the game favor and what is the probability of winning?"
Thank you so much for your help!