A strand of 100 lights is placed on a tree. At first, all of the lights are on. A second later, every other light change its state, thus shutting off. Another second later, every third light change its state, lighting if it was off and shutting off if it was on. Another second later, every fourth light change its state in the same manner, and so on. Find the probability that, after 100 seconds, a randomly chosen light will be lit.