For some reason, you must enter an even wager for $1 — win or lose — on one of two outcomes, but there’s a twist: Instead of a fifty-fifty choice like a coin toss, or picking 1-3 or 4-6, this one is pretty easy. Using a fair die (not crooked or “funny” in any way), you can bet that it will show 1,2,3, or 4 on the one hand, or you can bet that it will show 5 or 6 on the other. Those are your choices — 1-4, or 5-6. You know that if you had to do this a hundred times, you would come out money ahead by standing on 1-4, as this will win two times of three.
However, you only have one swing at this. Probably you will still choose 1-4. If you disagree, please let me know why. Assuming that you choose 1-4, there are only two outcomes. Obviously if you win with 1-4, you have chosen correctly. However, if you lose, because in your only throw, the die came up 5-6 — were you wrong?
Huh?
That is the most helpful, least sought feedback a writer can get :-)
It’s early here in AZ.
I am reminded of a quote I took to heart in my youth — “A joke that needs explaining needs burning”. That is, it’s not the listener’s fault if he doesn;t get a joke. BURDEN ON THE TELLER of the joke to judge the audience and adjust accordingly. Part of being clever is being clever about being clever.
Likewise, advice I have tried to honor is that if your writing is unclear (unintentionally), then you should re-write it. So I have expanded the first paragraph.
Thank you both for the feedback!
Question 1: How can a die with 2 possible outcomes where the likelihood of the outcomes are 1/3 and 2/3 be a ‘fair’ die?
What I intend here is to specify that the die is fair, and offer two options — you can cover 1-4, or 5-6. The die itself is fair — it’s the wager that is unrealistic.
If you only have the capital for a single wager, you are not wrong to bet on the outcome with the 2/3 likelihood of winning, however with only one opportunity this still becomes a binary outcome. A single wager and you are either still in the game with $2 on a positive outcome or out of the game all together.
The question becomes vastly more interesting with 3 $1 bills to wager and then allocating capital, managing, and so forth to stay in the game.
They still make two dollar bills?
Yup. Go to your bank and ask for them. Often they are brand new.
Time to confuse cashiers!
I usually carry some with me. I’ve been accused of trying to pass counterfeit currency.
Like!
I ALWAYS carry about 10. I leave them in addition to the regular tip if I liked the service. People notice and remember.
Indeed. Well played.
People all over Dallas know me because of $2 bills.
SO back to the question. You bet on 1-4, but it came up (say) 5. Were you wrong?
No. You just didn’t win.
What is this, the Mensa test?
Probably. I hope our membership doesn’t depend on our understanding the question let alone getting the answer correct!
I fervently hope not, too…
I don’t gamble and I’m math-phobic, but I agree w/M; you didn’t win, no rectitude/wreckeditdude at play here. (-:
Nanda, I don’t gamble either, and that’s because I like math :-)
I get you, beloved Admin, ISWYDT
EThompson? Your answer?