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?