Geometric Distribution

P(no car passes through the junction in 10 s) = (1 - 0.25)10 = 0.05631

When the pedestrain crosses the road at the end of 10th sec, he/she needs to wait a further 2 secs or less so that the event "has to wait for no more that 12 sec" comes true.

So for the next 2 secs, the prob. that there will be at least 1 car passing through the junction in both secs is 0.252 = 0.0625

Therefore the required probability is 1 - 0.0625 = 0.9375

2010-12-13 20:39:55 補充：
P(Wait for 10 s) = 0.05631
P(Wait for 11 s) = 0.25 x 0.05631
P(Wait for 12 s) = 0.25 x 0.05631 (since the first sec does not affect the decision at the end of 12th sec)

So total prob. = 0.05631 x (1 + 0.25 + 0.25) = 0.0845

The meaning of the question is that the pedestrian has to wait 10, 11 or 12 second before he cross the road.