Mice on a drawbridge; conditional probability.

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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.
 
Can someone help me think this through. Let's change the scenario. The blind mouse starts from the center of the drawbrige looking forward. She moves left and right but never backwards. She would cross the first level, on average, at the center of the drawbridge, left to right. Where she crosses the first level would have a normal distribution, with mean at enter of the drawbridge. Now the right-sided gap is no longer 10% of the width but is set so the mouse falls through the gap 10% of the time. The next right-sided gap at level 2 is now set so that the mouse falls through the gap 15% of the time with the assumption that crossing the second level would be normally distributed.

So, if there were no gap at the first level, the mouse would cross the second level 85% of the time. So now the question is more clear: How much less than 85% of the time would she pass level 2 with a gap now present at level 1. Another way to think this is: What is the chance that the mouse would have crossed level 1 in the 10% fail rate area and then have shifted left to pass in the 85% pass area. This sequence of events represents the small difference above 15% that only failed because there was a gap at level 1. Most of the time, if the mouse fails at level 1, then she would likely fail at level 2. But not all the time. This is a conditional question. What more data is needed?
 

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