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# Don't think too quickly

Wed 26 Mar, 2003 08:28 am
Suppose I flip two coins, without letting you see the outcome, and I tell you that at least one of the coins came up heads, what is the probability that the other coin is also heads?

Im getting better........................
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Type: Discussion • Score: 1 • Views: 4,800 • Replies: 36
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Slappy Doo Hoo

1
Wed 26 Mar, 2003 09:52 am
50%?
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Equus

1
Wed 26 Mar, 2003 09:58 am
If we assume you are telling the truth, there is a 33-1/3 percent probability that the other coin is also heads.

When you tossed the coin, there were four equally likely possible outcomes:
Tails-Tails
Since it wasn't Tails-Tails, there are now three equally likely outcomes, only one of which is both Heads.
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dlowan

1
Wed 26 Mar, 2003 02:39 pm
I go with 50%
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Craven de Kere

1
Wed 26 Mar, 2003 02:45 pm
Equus,

The result of one flip doesn't affect the result of the other.
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Craven de Kere

1
Wed 26 Mar, 2003 02:46 pm
Blaine,

What was the riddle that stumped you BTW? Those are some of my favorite books.
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cicerone imposter

1
Wed 26 Mar, 2003 03:01 pm
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Equus

1
Wed 26 Mar, 2003 04:43 pm
Okay, I guess I won't be playing any three-card-monty today.
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SealPoet

1
Wed 26 Mar, 2003 04:49 pm
CdK... ahh... the result of one flip doesn't affect the other perhaps, but Blaine isn't acting in a random fasion. Equus's reasoning is valid and sound.

Try it yourself with two different coins.

33 1/3%
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Craven de Kere

1
Wed 26 Mar, 2003 05:04 pm
SP,

I respectfully disagree. This is a very common error when calculating probability (to include initial probability with the secondary one).

The question is about 1 coin flip, not two (because the first flip has already been determined). Regardless of what the first coin's result was the other coin's probability is 50/50 (assuming that the coin is symmetrical.
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Heeven

1
Wed 26 Mar, 2003 05:06 pm
If neither coin had been flipped, I'd go with Equus's reasoning on the outcome, but since the result of one has already been revealed then I am leaning more towards slappys probability of 50%.
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Heeven

1
Wed 26 Mar, 2003 05:07 pm
Doh! Mr. Craven beats me to it!
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BillW

1
Wed 26 Mar, 2003 05:13 pm
One coin has been flipped with a known out come - heads; that's a given and can not be changed.

Another coin has been flipped with an unknown outcome; either heads or tails (not allowing that it ends on its side) -

probablity of 50%
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SealPoet

1
Wed 26 Mar, 2003 08:40 pm
But which coin is heads? Is it the dime or the nickle? He's not telling you, and if NEITHER coin had been heads he wouldn't have said so.

There are four possible (and equally likely) results of tossing two coins. For the sake of argument, one is a nickle and one is a dime.

Nickle is heads, Dime is tails and he says one coin (at least) is heads.

Nickle is tails, Dime is heads and he says (can you guess?) one coin (at least) is heads.

Nickle is tails, Dime is tails. Blaine don't say nuthin'. Or Blaine says at least one coin is tails. Or Slappy Doo Hoo says one coin at least is heads and gimme both.

There are three equally likely outcomes of the coin toss here. Not four, since tails-tails may be eliminated.

Of those three, only one yields the second Heads. 1 out of 3. 33 1/3%

Like he said... don't answer too fast.
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SealPoet

1
Wed 26 Mar, 2003 08:43 pm
Here's a related question.

On Let's Make A Deal... Monty Hall tells you there is a grand prize behind one of three curtains. You must choose one.

Monty has has lovely Carrol Merril show you whats behind a different curtain. It's a dud... a box of used food or something. Then he asks you if you would like to change your choice to the remaining curtain.

Do you or don't you? Why or why not?
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Craven de Kere

1
Wed 26 Mar, 2003 08:48 pm
Blaine The Mono wrote:
Suppose I flip two coins, without letting you see the outcome, and I tell you that at least one of the coins came up heads, what is the probability that the other coin is also heads?

I read that as saying there is no possibility of a tails/tails. "At least one of the coins came up heads".

I also don't see the relevance of which one is heads or tails.

I could be wrong but really don't think so.
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fbaezer

1
Wed 26 Mar, 2003 08:50 pm
Equus is right.
The key is the wording of the question.
It doesn't say, "if one coin comes up heads, what is the probability of the other one coming up heads?"; it says "if at least one of the coins came up heads".

If we have coin A and coin B,
"One coin" is coin A, "the other one" is coin B"
"At least one of the coins" is either coin A or coin B; the other one is, oh well, the other one.

Equus wrote:

"When you tossed the coin, there were four equally likely possible outcomes:
Tails-Tails".

In the first wording, the two latter outcomes are discarded.
In the second wording, only the last outcome is discarded.
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Craven de Kere

1
Wed 26 Mar, 2003 09:00 pm
Marilyn Vos Savant has long argued that point too fbaezer. I've always disagreed with her but I'll mull it.
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Craven de Kere

1
Wed 26 Mar, 2003 09:27 pm
Ok, I give. But many others still don't.

http://www.wiskit.com/marilyn/boys.html

http://www.geocities.com/SiliconValley/Circuit/1308/question.html
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Craven de Kere

1
Wed 26 Mar, 2003 10:30 pm
If only this one was worded like the original one that started the modern revival of this I could have held on for longre.

Here is a good one from Marilyn's ordeal.

http://www.geocities.com/SiliconValley/Circuit/1308/MoritzGrayPaper.html
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