New Sailing puzzle

[Catigale]

That last one was so much fun I just couldnt resist this twisted one..

Christoper Columbus is getting ready to leave to (unknown for him) discover a new Walmart in the New World and has to choose one of his three ships (the Nina, the Pinta, and the Santa Maria) in which to ride

One of them has all the food, while the other two have no food but are stuffed with West Marine Sailing gadgets to trade with the locals for spices and other good stuff.

Being an Old World Sailor, Christoper knows the guys on the boat with the food have the best chance of living if you are becalmed.

The Problem is, Christopher doesnt know which one has the food, and he wont get to choose until he is down on the docks in front of Queen Latifa and King George. He is a shrewd operator and enlists the help of his trusted Father Guido Sarducci (who never lies) Guido agrees to stow away on one of the boats and give him a sign if that boat has food.

Christopher arrives on the docks the following morning amidst the fanfare of trumpets.

Queen Latifa asks him...Which Boat will you ride in??

He desperately looks for Father Guido but he is no where to be seen. He casts his fate to the Gods and says:

"I choose the Pinta"

But then Father Guido pops up on the Nina and shakes his head (no food on the Nina).

Christopher thinks quickly.......I change my mind, I choose the Santa Maria...he says.

Do you think Christopher was smart??

[Beam's Reach]

It's way too early in the morning to be doing logic puzzles . But I sure enjoyed the story .

Can't wait to hear the end. Does Chris land on Fraggle Rock, meet the Explorer Formerly known as Ponce and discover the Fountain of Three Coins? Does he find the North West Marine Passage in time to celebrate Halloween with the Incas? Should I have paid more attention in history class?

[LOUIS B HOLUB]

HISTORY doesnt record the fact that CHRIS telegraphed home after finding the NEW WORLD. His message is kinda obscured due to "HAND DOWN" versions...but it went something like this: ....Arrived Well; found plenty of bargains at the Super Wal Mart; nice GREETERs too; I traded UP for 3 NEW plastic boats from an INDIAN fella by the name of ROGER; I can make the trip back home in less than 2 days NOW.

[Gerald Gordon]

BIG MISTAKE!

Cristobal Colon misread the names of the ships. It was not the Pinta. It was the Pita. This ship would later be the namesake of the now famous pita bread. So there...

[Catigale]

Gerald...


Ok - Im calling this one. We have two smarties here on the Board plus two people whose heads hurt

This is my favourite math problem of all, I think. It took the smartest guy I ever met in life, a Theoretical Stat Mech Physicist 30 minutes to figure it out.

Answer one (Chris is a smart dude) and Four (The food is twice as likely to be on the Santa Maria than the Pinta are correct.

Who claims the two gybing Blue Centerboards for their prizes?

[Sjack]

Catigale,

You got some "splainin" to do on this one.

I don't buy it.

[Gerald Gordon]

Theoretical Stat Mech Physicist!!! That sounds impressive, but that's nothing compared to what I have to figure out to get my girlfriend diamond studs for x-mas and give them to here on our December Gulf cruise!!!

[Catigale]

OK - Ill try, but I confess I suck at explaining this one in a clear manner.

To recap, the food is one of three boats, and Christopher chooses one.

His chance of choosing the correct boat is 1 out of 3 - everyone ok with that??

Equally important, his chance of not picking the food is 2/3...everyone ok with that??

Now, he has chosen one. He gets additional information that one of the other boats (but not the one he chose) DOES NOT have the food.

The puzzle question is, is it a good strategy to switch from the boat you first chose, to the last remaining boat.

Well it is.

Let suppose he has chosen the food, and does not switch. His chance of winning is 1/3 - unchanged.

Lets suppose he has chosen the food and he does switch. He loses, but there is still only a 1/3 chance of losing this way (the same chance of choosing the food in the first place)

..and now the drum roll

If he hasnt chosen the food,and he switches HE WINS!! (Since in this case, he didnt choose the food, and we threw one boat out from additional information, the food MUST be on the 'third boat')

But what are the odds of choosing this scenario?? THe same as the odds of NOT choosing the food in the first place...or 2/3

So, if he switches after getting the additional information, he DOUBLES his chance of getting the food from 1/3 to 2/3.

Sidebar - this puzzle seems to violate principles of probability, however, its very sneaky. Bringing in the additional information after you chose effectively resets the probabilities because it changes the probability of the food being on the boat after you chose it, if you will.

It sort of like buying a 1 in a million chance lottery ticket, then being told that all but you and one other ticket holder have losing tickets...your chance of winning changes, even though your initial chance was 1 in a million.

[kmclemore]

This is the classic "Let's Make A Deal" statistical probability problem, and it's been around for ages.... it's explained pretty well in a couple of places on the 'net and at some you can even play it 'live' to experience it for yourself:

http://www.stat.berkeley.edu/users/star ... t/ch10.htm

http://www.stat.sc.edu/~west/javahtml/L ... aDeal.html

[DLT]

I may be missing something, but how does conditional probability apply to the stated problem?

Wouldn't there have to be some relationship between the initially chosen ship and the one that Father Guido pops up from? Isn't that what makes it conditional?

In the game show example, the host is required to choose one of the two not initially selected.

But here, when the initial choice is made, Chris has no idea where Father Guido is. Father Guido is already hidden below deck on one of the three. In other words, Father Guido is already where he is, when Chris chooses. Father Guido just so happens to appear on one of the ships Chris didn't choose. If Chris would have chosen the Nina, Father Guido would have still popped up there. This is the major difference in using conditional probability here.

If Father Guido would have boarded and inspected a ship after Chris' initial choice, then we'd be back to conditional probability...

[Catigale]

Its crucial that you get the additional information about one of the ships you did NOT choose, correct. If you were told, sorry, your ship has no food, but you can choose again, your chances would then be 1/2 to win, a simple choice of two boxes.

[Chip Hindes]

Before the Father Guido report:

His chance of choosing the correct boat is 1 out of 3 - everyone ok with that??

Equally important, his chance of not picking the food is 2/3...everyone ok with that??

Correct. Then he gets addtional information. One of the boats is eliminated from the problem completely. It's now a new problem.

Let suppose he has chosen the food, and does not switch. His chance of winning is 1/3 - unchanged.

Nope. One boat is elimnated, gone, kaput, out of the equation. There now only two boats, are only four possible outcomes. He switches, he's wrong, he loses. He switches he's right, he wins. He doesn't switch he's wrong, he loses. He doesn't switch, he's right he wins. Two outcomes are favorable, two are unfavorable. 2/4, 1/2, 50%, however you cut it.

[Hamin' X]

I gotta agree with Chip on this one. It's the old problem of being able to prove anything with statistics. It becomes a matter of perspective. Like this one. I flip a coin 99 times and it comes up heads everytime(yes it has a tails side). What are the odds of it comming up heads on the 100th flip? Exactly 50/50.

Chris's odds at the time he chose to switch, were 50/50. In the real world, what happens next is what you need to worry about.

[kmclemore]

Yeah, and everyone knows that 43.5% of all statistics are made up on the spot anyway.

[Catigale]

Thats only true 99 44/100% of the time Kevin