Probability of a watched clock changing.

[BonJoviJones]

This is a generic probability question I came up with while watching the digital clock in my car waiting for it to warm up:

You look at a digital clock (that doesn't display seconds) for 1 second. What is the chance that it changes in that second? Assuming it doesn't change and you continue to observe it, what is the chance it changes in the following second... and the following second... etc etc.

I think it's pretty clear that for the first second the chance is 1 in 60. Also, while observing on the 60th second, it _must_ change. This implies P(change) is 1/n, where n is (60 - the number of seconds observed).

Can anyone answer for sure?

Thanks.