Thanks, now I understand how they reached the number but not why it's so convoluted. I only took one stats course in college.

So it's

P(bomb exploding in a century) = 1 - P(bomb not exploding in a century) = 1 - (P(bomb not exploding in a year)) ^ 100 = 1 - (1 - P(bomb exploding in a year)) ^ 100

Why is it not something simpler, like P(bomb exploding in a year) ^ 100 ?