Penelope the Pessimist and Olivia the Optimist are two of ten finalists in a contest. One of these ten finalists will be randomly chosen to receive the grand prize (all finalists have the same chance...

Penelope the Pessimist and Olivia the Optimist are two of ten finalists in a contest. One of these ten finalists will be randomly chosen to receive the grand prize (all finalists have the same chance of winning). Just before the grand prize is awarded, a judge tells eight of the finalists that they have not won the grand prize, and only Penelope and Olivia remain. Penelope thinks: Even before the judge eliminated the eight contestants, I knew that at least eight of the other people were losers. That I now know that those eight are losers doesn’t tell me anything. My chance of winning is still only 10%. What rotten luck! Olivia thinks: Now that those eight have been eliminated, there are only two of us left in the contest. So now I have a 50% chance of winning. What wonderful luck! Whose analysis is correct?