Olivia loves cookies so much that Dad promises to buy her two cookie jars on one condition: that she only eats one cookie per day.
Olivia agrees, and now two black, large cookie jars rest on the kitchen table. The jars are completely opaque, but on the label it says very clearly: each jar contains exactly 100 cookies.
So every morning Olivia wakes up, randomly selects one of the cookie jars, opens it and takes one cookie. Yum. Nobody else in the house eats cookies, so she's in for a long time treat.
After some time though, the inevitable happens: when Olivia opens the randomly selected jar that morning, she finds that the jar is empty. Quickly she glances worried to the other jar and the question pops into her mind:
What is the probability that the other jar is also empty?
EDIT: For clarification, Olivia does not realise that a jar is empty when taking the last cookie from it.