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Active: 750 users

Lack of sanity

Blogs > helpman170
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helpman170
Profile Blog Joined May 2015
34 Posts
May 09 2015 13:25 GMT
#1
There is a box with two coins.
One coin is heads on one side and tails on the other side.
The other coin is heads on both sides.

You draw one coin at random and it is heads.
What is the probability that the other side is heads?

***
Saechiis
Profile Blog Joined May 2010
Netherlands4989 Posts
May 09 2015 13:55 GMT
#2
50% ?
I think esports is pretty nice.
Ovid
Profile Blog Joined October 2013
United Kingdom948 Posts
May 09 2015 13:57 GMT
#3
50%
I will make Yogg Saron priest work...
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 14:00 GMT
#4
I have a feeling it isn't but I haven't looked into the maths yet.

If you select a coin and it has heads then isn't it more likely that the coin you have is the one with 2 heads, therefore it is higher than 50% that the other side is heads?
Zerg for Life
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 14:04 GMT
#5
like P(2nd face heads / 1st face heads) = P (1st face heads and 2nd face heads) / P(1st face heads)

= 0.5 / 0.75

= 0.667

66% chance
Zerg for Life
Saechiis
Profile Blog Joined May 2010
Netherlands4989 Posts
May 09 2015 14:17 GMT
#6
I don't math. But my thought was that if you get the double heads coin it's always heads on the other side and if you get the split side coin it's always tails on the other side. It's 50% to get either coin.
I think esports is pretty nice.
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 14:20 GMT
#7
On May 09 2015 23:17 Saechiis wrote:
I don't math. But my thought was that if you get the double heads coin it's always heads on the other side and if you get the split side coin it's always tails on the other side. It's 50% to get either coin.


the fact that you pulled a heads on the first coin means you have to use conditional probability.

in english words, because the first face is heads you have more than likely pulled the coin with both heads.

I think

Zerg for Life
Ej_
Profile Blog Joined January 2013
47656 Posts
Last Edited: 2015-05-09 14:24:23
May 09 2015 14:21 GMT
#8
H`, H ...... T H
H`, H ...... H T
H, H` ..... T H
H, H` ..... H T
T, H ..... H`, H
T, H ...... H, H`

H, T ....... H`, H
H, T ....... H, H`


exactly half of the events are a solution though? I marked the coin with only heads as having H and H`. Could someone good at maths explain what I'm missing here?

e: I guess what Kelsier just said makes sense, then indeed it is 2/3
"Technically the dictionary has zero authority on the meaning or words" - Rodya
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 14:23 GMT
#9
events 5 and 6 aren't considered because we are told the first face is heads
Zerg for Life
Saechiis
Profile Blog Joined May 2010
Netherlands4989 Posts
May 09 2015 14:37 GMT
#10
I think you're right KelsierSC.
I think esports is pretty nice.
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 14:40 GMT
#11
On May 09 2015 23:37 Saechiis wrote:
I think you're right KelsierSC.


there's always a first time.
Zerg for Life
Ovid
Profile Blog Joined October 2013
United Kingdom948 Posts
May 09 2015 16:55 GMT
#12
On May 09 2015 23:04 KelsierSC wrote:
66% chance


That makes sense because of the wording (since you're quantifying that is has to be the double heads coin you pick out not getting a heads on the otherside as an outcome)

It's 75% of the time you're going to pick out heads to start and 50% chance for the next outcome so 66% is right just didn't read that the parameter is you've got to have picked out heads to start with.
I will make Yogg Saron priest work...
LegalLord
Profile Blog Joined April 2013
United Kingdom13775 Posts
Last Edited: 2015-05-09 17:21:32
May 09 2015 17:18 GMT
#13
KelsierSC is correct. In general:
P(A and B) = P(A given B) * P(B)

Do the math and you get the result that he got.
More information: http://en.wikipedia.org/wiki/Bayes'_rule
History will sooner or later sweep the European Union away without mercy.
Yorbon
Profile Joined December 2011
Netherlands4272 Posts
May 09 2015 18:15 GMT
#14
What's the connection between this problem and (a lack of) sanity?
IAmWithStupid
Profile Blog Joined February 2013
Russian Federation1016 Posts
May 09 2015 18:43 GMT
#15
mathematician asks a blonde: "what are the chances of going out and seeing alive dinosaur?" She responds: "50%: either i'll see it or I won't"
Insert wise words here
JieXian
Profile Blog Joined August 2008
Malaysia4677 Posts
Last Edited: 2015-05-09 18:56:27
May 09 2015 18:49 GMT
#16
Edit: never mind I misunderstood the question, I thought it was about flipping one coin and getting heads, then flipping the other coin.

I thought it was 75%?

If the first coin is already heads, the actual problem changes to:

I have 2 coins, one of them has heads on both sides and one of them has heads on one side and tails on the other. I pick one of them at random and flip it. What is the possibility of it coming up heads?

so for coin 1 and coin 2 the possibilities are:

h1 , h'1 , h2, t2
P(h) = 0.75
Please send me a PM of any song you like that I most probably never heard of! I am looking for people to chat about writing and producing music | https://www.youtube.com/watch?v=noD-bsOcxuU |
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
Last Edited: 2015-05-09 19:25:15
May 09 2015 19:22 GMT
#17
On May 10 2015 03:49 JieXian wrote:
Edit: never mind I misunderstood the question, I thought it was about flipping one coin and getting heads, then flipping the other coin.

I thought it was 75%?

If the first coin is already heads, the actual problem changes to:

I have 2 coins, one of them has heads on both sides and one of them has heads on one side and tails on the other. I pick one of them at random and flip it. What is the possibility of it coming up heads?

so for coin 1 and coin 2 the possibilities are:

h1 , h'1 , h2, t2
P(h) = 0.75


you have neglected the fact that the first face is heads.

edit - didn't see edit
Zerg for Life
OtherWorld
Profile Blog Joined October 2013
France17333 Posts
May 09 2015 19:56 GMT
#18
It's indeed 2/3, but I don't get where the lack of sanity is d:
Used Sigs - New Sigs - Cheap Sigs - Buy the Best Cheap Sig near You at www.cheapsigforsale.com
KelsierSC
Profile Blog Joined March 2013
United Kingdom10443 Posts
May 09 2015 19:57 GMT
#19
On May 10 2015 04:56 OtherWorld wrote:
It's indeed 2/3, but I don't get where the lack of sanity is d:


I'm guessing the OP was having issues with the problem.

seems like he has left after we did his homework
Zerg for Life
riotjune
Profile Blog Joined January 2008
United States3393 Posts
May 10 2015 00:26 GMT
#20
I'm a layman and I already knew some little shit was going to get me in this scenario. This time it was named "conditional probability."
spinesheath
Profile Blog Joined June 2009
Germany8679 Posts
May 10 2015 06:28 GMT
#21
Sounds very similar to the Monty Hall problem.
If you have a good reason to disagree with the above, please tell me. Thank you.
YokoKano
Profile Blog Joined July 2012
United States612 Posts
May 10 2015 08:52 GMT
#22
c0nned
IQ 155.905638752
_fool
Profile Joined February 2011
Netherlands677 Posts
May 10 2015 21:20 GMT
#23
2/3rds
"News is to the mind what sugar is to the body"
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