Fog Creek Software
Discussion Board




painfully easy

the answer should be 50%, because the chance of the other coin landing heads or tails is not dependant on the result of the other coin.

Jonathan Davisson
Sunday, October 10, 2004

No, Gerd was right, on the other thread in this topic. You're confusing the knowledge that some *specific* coin (e.g, the first, or the second) was heads with the knowledge that at least *one* coin was heads (without the knowledge which that is).

Do an experiment (use a computer if you can, or a coin if you can't): Flip two coins (or simulate two coin flips) 30 times. Now, select, of those flips, only the ones where at least one is heads (don't just select ones where the first is heads, or where the second is heads--select both groups). You'll see that, of those, around 1/3 have the other coin on heads too.

Avrom Roy-Faderman
Monday, October 11, 2004

No the sotution should be 50%; In the table, there are four heads the flipper could be telling me about, and for two of them, the other coin is heads.

penny/dime
1.HH
2.HT
3.TH

In case one, the flipper could be telling me the penny is heads, or the dime is heads.

Steamrolla
Thursday, October 21, 2004

Yes, but that doesn't matter. 1/2 the *heads* are in case 1, but only 1/3 the *cases* are case 1.

Like I said, do the experiment. You will find that, while half the heads are in "HH" pairs, only 1/3 the pairs containing heads are "HH" pairs.

Avrom Roy-Faderman
Thursday, October 21, 2004

I think it should be 50% because  among the cases
HT
TH
you should consider both of them to be the same. When you simulate on a computer as someone said we should, even then we should consider them to be the same. If you consider those two cases different then you're introducing dependencies which you can't because as we all know from HIGH SCHOOL mathematics that the two coins are independent.

So now if you look at  the cases

HH
HT (same as TH)
The answer should be 1/2.

Varun Pandey
Saturday, November 27, 2004

Call the coins Coin A and Coin B.

"Coin A is heads; Coin B is tails" and "Coin A is tails; Coin B is heads" are different situations. There's no two ways about this.

Like I said, do the experiment--it's really easy; it will take 5 minutes of your time, at most. There's no "considering" to be done here. You'll see the cases divided as follows:

1/4 HH
1/4 HT
1/4 TH
[or just "1/2 one head, one tail", if you don't want to keep track of which coin is which]
1/4 TT

(that is, 3/4 will have at least one head, and of those, 1/3 will have both).

Avrom Roy-Faderman
Wednesday, December 22, 2004

1/3 is the generally accepted answer.

But it depends on the questioner. Does he tell you that one of the coins is heads whenever either of them is? Then it's 1/3.

Does he tell you one of them is heads whenever the dime is heads?  Then it's 1/2.

Does he tell you one of them is heads whenever he feels like it, provided one of them is heads?  Then it could be anything from 0 to 1.  To get an answer of 1/3 or 1/2 you have to assume that the questioner is unbiased.

J Thomas
Saturday, December 25, 2004

The answer is 1/3 only if the person doing the flipping decides upon "heads" before flipping, then reflip the coins if they both came up tails.

However, if the person doing the flipping simply picks a coin (at random or otherwise) and announces it's value after the flipping, the answer is 1/2.

Markus Persson
Monday, January 03, 2005

*  Recent Topics

*  Fog Creek Home