Poll

1 vote (1.88%)
1 vote (1.88%)
13 votes (24.52%)
32 votes (60.37%)
1 vote (1.88%)
1 vote (1.88%)
4 votes (7.54%)

53 members have voted

rdw4potus
rdw4potus
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May 17th, 2011 at 8:55:08 PM permalink
Quote: kp


If you pull a coin from the box that has heads up, what is the chance that the other side will have heads? 2/3.

If you already have one of the two coins in your hand and it has heads up, what is the chance the other side is heads? 1/2.



I don't see where you've gained any additional information between these two examples. Either way, you're just looking at the heads side of one of two coins.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
vert1276
vert1276
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May 17th, 2011 at 9:01:30 PM permalink
Quote: kp

My first answer was 2/3. Then I doodled on paper and came up with 2/3. Now a couple of days later I'm switching to 1/2.

If you pull a coin from the box that has heads up, what is the chance that the other side will have heads? 2/3.

If you already have one of the two coins in your hand and it has heads up, what is the chance the other side is heads? 1/2.

The first scenario is a compound event (parlay). The second scenario is an independent trial.



I feel like Darth Vader and im turning people to the dark side of 1/2 LOL!!!!!!!
Face
Administrator
Face
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May 17th, 2011 at 9:19:40 PM permalink
Quote: vert1276

LMAO I know you guys think im totally messin with you but im not.



And I was just foolin' when I accused you of being tuttigym. But seriously, I'm having flashbacks. =)

Your points are good enough that I'm going back to examine the original question, but then again, I'm one of the one's who think picking the other door in Monty is pointless =P

Edit: Nevermind. 10 seconds and I think 2/3 too. Still wouldn't pick the other door though.
The opinions of this moderator are for entertainment purposes only.
MathExtremist
MathExtremist
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May 17th, 2011 at 9:44:12 PM permalink
Quote: vert1276

1) I know there is at least one American flag stamp still in the box, correct?
2) I know the American flag stamp I am "observing" can not also be on the other side of the quarter, correct?
3) I still have 2 possible postage stamps that can be on the other side of the quarter, correct?

Now you all are saying there is a 66% chance the other side of the quarter has an American flag stamp on it. And Im saying there is only 2 possibility left now that I have observed one face and one of the 2 has to be the liberty bell stamp. please explain to me how there can be 3 possibilities left to be other the other side of the coin WITHOUT reaching back into the box?


Don't confuse possibility with probability. There are only two possibilities because there are only two images -- flag or bell. But the flag is twice as likely as the bell.

This has been suggested before (bird/fish/etc. analogy) but when you distinguish the sides it becomes easy, I hope. If you number the heads 1, 2, and 3, but you apply them randomly to the coins, you can either have
H1/H2, H3/T
or
H1/H3, H2/T
or
H1/T, H2/H3

Let's suppose I do that and put the coins into a bag, and I chose the arrangement randomly with equal probability from the above possibilities. You reach into the bag and pull out a coin with H1 showing. What are the chances that the flip side is either H2 *or* H3?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
cclub79
cclub79
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May 18th, 2011 at 4:49:19 AM permalink
Quote: MathExtremist

Don't confuse possibility with probability. There are only two possibilities because there are only two images -- flag or bell. But the flag is twice as likely as the bell.

This has been suggested before (bird/fish/etc. analogy) but when you distinguish the sides it becomes easy, I hope. If you number the heads 1, 2, and 3, but you apply them randomly to the coins, you can either have
H1/H2, H3/T
or
H1/H3, H2/T
or
H1/T, H2/H3

Let's suppose I do that and put the coins into a bag, and I chose the arrangement randomly with equal probability from the above possibilities. You reach into the bag and pull out a coin with H1 showing. What are the chances that the flip side is either H2 *or* H3?



Said that Monday, too. We're just going to keep using the same arguments, so I'm with Mosca. The 4th graders that weren't convinced did the experiment and ended up with "Heads" around 65-70% of the time. If you don't want to do that, we're just going to be arguing in circles.
DJTeddyBear
DJTeddyBear
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May 18th, 2011 at 6:06:33 AM permalink
Maybe I'm oversimplifying things but....

I haven't read ANY of the responses since I was the first responder on page 1.

As I see it, past results have no influence on future actions.

You either pulled the two-headed coin out or not.

So it's a 50% chance the flip side is heads.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
DJTeddyBear
DJTeddyBear
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May 18th, 2011 at 6:23:27 AM permalink
Apparently, I WAS oversimplifying things.

I started reading the thread. About half-way thru page 4, the fog cleared.

I then went back to page 2, to re-read this little comment in ChesterDog's Post:
Quote: ChesterDog

What's the probability of first seeing a randomly-selected coin as heads and then finding out that the coin is double-headed?

Yeah, phrased that way, it's obviously 2/3.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
HKrandom
HKrandom
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May 18th, 2011 at 6:57:24 AM permalink
Quote: DJTeddyBear

Maybe I'm oversimplifying things but....

I haven't read ANY of the responses since I was the first responder on page 1.

As I see it, past results have no influence on future actions.

You either pulled the two-headed coin out or not.

So it's a 50% chance the flip side is heads.



If you pull a coin a million times, 25% of the time you will pull the normal coin on the tail side, 25% of the time you would pick it on the head side and 50% of the time you would get the other coin on head. These are your 4 possibilities:

Double headed coin, heads.
Double headed coin, heads.
Regular coin, heads.
Regular coin, tails.

Now let's take out the last possibility.
Double headed coin, heads.
Double headed coin, heads.
Regular coin, heads.
Regular coin, tails.

There are now 3 possibilities, two of which are that you picked the double headed coin.
DJTeddyBear
DJTeddyBear
Joined: Nov 2, 2009
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May 18th, 2011 at 7:55:28 AM permalink
HK -

Yeah, I know. I already did a follow-up.

And I've also come up with a simpler response:

There are three faces that are heads. You could have picked any one of them. Two of them have heads on the other face, therefore, 2/3 of the time it's the double headed coin.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
MathExtremist
MathExtremist
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May 18th, 2011 at 8:06:12 AM permalink
Quote: cclub79

Said that Monday, too. We're just going to keep using the same arguments, so I'm with Mosca. The 4th graders that weren't convinced did the experiment and ended up with "Heads" around 65-70% of the time. If you don't want to do that, we're just going to be arguing in circles.


And since I don't like arguing in circles, I'll simply offer this:

I'll gladly offer anyone a wager of $100 to my $130 that *tails* will show when we play the game. If the odds of heads or tails are truly 1/2, that yields a healthy +15% EV. I'll play for as many trials as you want. Any takers?

(Of course, if I'm right, I have a +18% EV...)
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563

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