(a) You're on the game show, "It's Your Choice, Dummy." You've made it to the final round, and the host, Bobby Roberts, has three envelopes in his hand. He says, slyly, "These three envelopes have different amounts of money in them. The envelope with the most amount of money in it has twice as much money as the envelope with the middle amount of money; and the envelope with the middle amount of money has twice as much money as the envelope with the least amount of money."
"Pick an envelope and open it," Bobby says. You randomly pick one and tear it open. Inside is a check for $10,000. "You can either keep that envelope or exchange it for one of the other two," Bobby says. "It's your choice, dummy."
You start to think. "If this envelope has the least amount of money, and I switch, I have a 50 percent of $20,000 and a 50 percent chance at $40,000, or an average of a $30,000 take.
"If this envelope has the middle amount of money, and I switch, I have a 50 percent chance at $5,000 and a 50 percent chance at $20,000, or an average of a $12,500 take.
"If this envelope has the most amount of money, and I switch, I have a 50 percent chance at $2,500 and a 50 percent chance at $5,000, or an average of a $3,750 take.
"Since all these have an equal chance of happening -- one in three -- my expected value if I switch is one-third of $30,000 plus $12,500 plus $3,750. That'd be an expected value of $15,416.67, more than $5,000 than if I keep my original envelope!
"But wait. How can I know that I should switch envelopes if all I did was see how much money was inside?"
How did you go wrong? Or did you, dummy?
(b) Essay: Write a four-line, rhyming poem in iambic pentameter with a secondary anapestic foot. (Meterically, that's "dum DUM dum dum DUM dum DUM dum DUM dum DUM.")
The winner gets my broken office stapler.
oh so lovingly written by
Matthew |
i sincerely do not know what you are doing here. are you lost? were you
looking for your delicate calico cat, and did you follow her up two flights of stairs
to this room? she is not here. she was here, yes. we gave her a warm bowl of milk, we talked with her about campaign finance reform for a time, and then she bid us good day. i believe she was
going to the post office two blocks down, but i don't quite recall.
for surely you did
not find your way from prinsiana, the least traveled site on
the internet. if you did, though, perhaps you are looking for humor. perhaps you are looking for profundity. perhaps you are looking for answers.
i'm sorry, but you shall go naught-for-three.
