Thread: Brain teaser.

Originally Posted by switt775

Q2. You have amazed yourself and your friends by flipping 9 consecutive Heads. What are the odds that the 10th flip will be Heads?

I wont bother with question 1 but the answer to question 2 is 50/50. It is not dependent of the throws that preceded it.

If you wish to maintain that your analysis is correct, when it is analyzing the choices that Monty has and not the choices that his actions leave the contestant with, I have three cups and a little ball. Bring your money and come down for a little game.

Cheers

Doug

Originally Posted by doug3030

I wont bother with question 1 but the answer to question 2 is 50/50. It is not dependent of the throws that preceded it.

If you wish to maintain that your analysis is correct, when it is analyzing the choices that Monty has and not the choices that his actions leave the contestant with, I have three cups and a little ball. Bring your money and come down for a little game.

Cheers

Doug

Happy to Doug. As long as you follow Monty's rules.

I included the second puzzle because it illustrates the trap of using logic rather than math. You are correct, the chances of getting heads on any individual throw is 1/2, so the fact you've just rolled 9 consecutive heads is irrelevant. A coin has no memory. Many reason because the odds were so small at the beginning ( 1 in 1024) they must still be very low.

On the 1st puzzle, we will have to agree to disagree.

the difference is each throw is independent from all other throws.
The three doors are not independent, the prize is only behind 1 of the three.
And it makes no difference where the doors are in the puzzle, makes no difference if they open door 3 or door 2 to show a goat.
But I'll let you disagree anyway.

My rule explain it twice and if you still haven't got it, your on your own.

Originally Posted by switt775

Happy to Doug. As long as you follow Monty's rules.

Ok We will follow Monty's rules. I will be the contestant you can be Monty.You put up $50 as the prize for each game and I will pay you $50 for every game I lose.

To reiterate the rules from TT's initial post:

"You are presented with three doors.
Behind one of the doors is a new car.
Behind the other two doors are goats.

You are allowed to choose one of the doors but it isn’t opened yet.
Instead, the host of the show opens one of the other doors, to reveal a goat.
Two doors remain closed.
Host then gives you a choice:
A ) stick with your original door
or
B ) switch to the other unopened door instead.
The first is that the car is always placed randomly amongst the three doors.
Second, the host always knows where the car is.
The third is that the host will always open a door to reveal a goat.
The last important detail is that the contestant (that’s you) knows all of this information ahead of time."

My rules: once you start you are committed to a minimum of 99 games. We woupd of course simulate the goats and cars with other objexts

If you come down bring at least $2000 cos statistically I stand to win $1650. It could be more if I get lucky. If you play the minimum 99 games I will refund your airfare, so long as its a normal domestic air fare, no sneaky travelling via Europe.

Of course if you are right then we should break even on the game but I will still pay your air fare.

Switt775 COME ON DOWN!

Cheers

Doug

actually, not on his own ... i'm with switt ... i concede my time with maths is probably now antique, but i DO favour maths over logic ever since primary school in the 1960s when a teacher tried to explain that one couldn't shoot a running rabbit with an arrow fired from a bow because by the time the arrow reached the position of the rabbit, it would have moved on a bit etc

of course if the rabbit was smart enough to run sideways, it might get away with it. but that's not how logic works

regards david

Chance of getting a good prize is 2/3. It must be a NZ game show.

Originally Posted by Wongo

Chance of getting a good prize is 2/3. It must be a NZ game show.

More than a game show, it is proof that people think emotionally not logically. Look at the 100 doors example referred to in TT's explanation. The contestant picks one box hoping it is the winner. The host then starts to open the other 99 boxes to reveal only losing boxes but he knows which are winners and which are losers. Every time the host opens a new box it is increasing the chance that the prize is still in one box that he has not opened but the contestant who has an emotional need to feel lucky and smart, sees it as reinforcement that he has chosen the right box right from the start. He does not consider that the chance of the host revealing the prize is ZERO because he knows where it is. He will only have the right box one time in 100 and the rest of the time the right box will be the last one left unopened by the host. Despite the odds against it it is human nature for people to think that with two boxes left to go its still 50/50 so I will hold on to what I have. "Wouldn't it be terrible if I picked the right box from the start and gave it away at the end?"

It makes no difference.

You are left with 2 choices and the odds are 50/50

Your 2 choices are,
1 - pick the one you did not pick
2 - pick the one you did pick

1 & 2 have equal chance so how do you get a better change by swtiching?

I am not gong to explain it any more. If you wish to disprove it let me know and take up the offer I made to Switt above and bring your money.

I understand how it works now. I missed the fact the host will always show the goat.

...but one goat...

And was it a good looking goat?

In the 100 door scenario, the two remaining doors both had a 1 in 100 chance of initially concealing the car. As the other 98 doors are opened, BOTH doors have their odds of concealing the car increase to.... well, what do you know?.....50% each.

The host cannot open your door if you have the car (he cannot open your door full stop) and he cannot open a door you did not choose if it conceals the car (prematurely stops the game.) Therefore, every show without fail, the host works his way through to two doors remaining. Half of the time, one door will have the car and you will have won; half of the time, still one door will have the car and you will have won...a goat. WIN WIN!!!

Actually there are only 10 possibilities no matter how many doors: either you win or you lose, so really the odds are 1 in 10.

(Of the 10 types of people in the world 1 will understand this deviation from topic and the other won't.)

Originally Posted by labr@

Actually there are only 10 possibilities no matter how many doors: either you win or you lose, so really the odds are 1 in 10.

(Of the 10 types of people in the world 1 will understand this deviation from topic and the other won't.)

Labr@, that is very naughty of you, bringing up that old thread (ok I admit I thought of doing that but some of them are having enough trouble with this one).

Congratulations on how smoothly you introduced it.

Cheers

Doug

EDIT: At least this way I wont get the blame this time