Michael is one of eight contestants entered in three races to be run on a eight-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?

That probability equals

1 - (prob. of never getting lane 1)
= 1 - (prob. of not getting lane 1 in a given race)^3

= 1 - (7/8)^3 = (512 - 343)/512
= 169/512 = 0.3301