Mice on a drawbridge; conditional probability.

A blind mouse has to pass two levels to cross a drawbridge. Bridge is uniform in width. At level 1, 10 % of the right side of the drawbrige has fallen off leaving a gap. At level 2, 15 % of the right side of the drawbridge has fallen away leaving a gap. What is the probably that the blind mouse pases both levels. Assume that aside from the two gaps, there is a rail on the drawbridge that keeps the mouse from falling off and that the mouse starts in the middle of the bridge and walks randomly in a forward direction across the bridge.

 

Interesting problem. It seems to me (but I may be wrong), that you need to clarify "randomly in a forward direction."

I assume by "middle of the bridge" you mean not yet on the bridge, but centered.

E.g., a 1 degree deviation from straight differs quite a but from an 89 degree deviation.

Also, if mouse starts one foot from the bridge vs. 100 feet, the initial deviation matters a great deal.

 

Yes, by middle of the bridge means that mouse is centered in the middle of the drawbridge left to right before stepping on the bridge. Assume the mouse moves left and right randomly but never moves backwards but always towards the other end of the bridge. The mouse zig zags but always moves forward. Assume that the point of crossing the first level would be the center of the drawbridge left to right for level 1. The question then becomes, what is the mean for crossing the second level? This is really a variation on the first question I suppose.