ggFTW

MMORPG Gamer Community


Go Back   ggFTW Forum > Off Topic > Life & Relationships > Homework Help

League of Legends
Looking for a new MMO?

Try 

League of Legends

Rating:  

8.3

 
LinkBack Thread Tools Display Modes
11-13-2008   #1 (permalink)
ggFTW Stalker
 
Join Date: Jul 2007
Location: In reckless abandon, I follow the Turtle.
Posts: 520
iTrader: (0)
sentythee is just really nicesentythee is just really nicesentythee is just really nicesentythee is just really nice
Guild: Titans
Default A man walks into a bar... (probability question)

I don't really need help with this, I just wanted to throw out a problem to see who could solve it, and this seemed like the best place to put it.
__________________________________________________ __________________________________________________
A man walks into a bar and claims that he has never yet lost money in a game of dice. The bartender clearly doesn't believe this man and so he challenges him. The bartender doesn't have a pair of dice on him, but he pulls out a perfectly-weighted quarter (50% chance of heads, 50% chance of tails).
"One cent is riding on this. Call it in the air."
The bartender flips the coin.
"Heads."
The coins shows heads.
Bartender: "Double or nothing."
The bartender flips again.
"Heads."
The coin shows heads again.
Bartender: "Double or nothing."

The bartender keeps flipping the coin, and the man keeps calling heads and winning. After 20 flips, the man stops the bartender.
"You've flipped the coin 20 times landed heads every single time. Let's try something different for the next Double-or-Nothing. I'll let you keep flipping the coin as many times as you like. If at any point you have managed to land twice as many tails as you have landed heads, I'll call off all the money you owe me. The 20 you've already flipped will still count against you."

The bartender accepts the challenge.

What is the probability that the bartender will lose the bet (never stop flipping the coin)?
__________________

Last edited by sentythee; 11-13-2008 at 09:15 PM.
 
Get rid of this ad by registering for our community.
11-13-2008   #2 (permalink)
ZeR
ggFTW Stalker
Special Games
La TaleDragon Nest
 
Join Date: Jun 2008
Location: Australia
Posts: 1,759
iTrader: (9)
ZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of light
Default

lol...

i would say the bartender will never lose. So 0.

If you multiply infinite times of 1/2 probability you'll just get 0. I was never good at probabililty at school so thats just a guess xD
 
11-13-2008   #3 (permalink)
Discuss.
Xpecial's Avatar
Games
League of LegendsAionAlliance of Valiant ArmsBloodline Champions
Awards Retired Forum ModeratorMoM Award
 
Join Date: Jun 2008
Location: California
Posts: 3,019
iTrader: (1)
Xpecial has disabled reputation
Send a message via AIM to Xpecial
IGN: Xpec
Class: Dainn lu_dainn
Level: -
Guild: -
Default

Theoretically, one can continue to flip the coin until that happens.

Probability wise, I think the chances of that is quite low as it would mean:

2 tails: 1 head (the closer this approaches infinity, the more accurate the requirement would be).

However, I have not taken any statistics class, so if there is some weird solution, don't kill me for being wrong.
__________________
 
11-13-2008   #4 (permalink)
Sexy Bish <3
Special
SkillzKillz's Avatar
 
Join Date: Jun 2008
Location: █♣█
Posts: 2,437
iTrader: (22)
SkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to beholdSkillzKillz is a splendid one to behold
Default

50 %
__________________

 
11-14-2008   #5 (permalink)
ggFTW Stalker
 
Join Date: Jul 2007
Location: In reckless abandon, I follow the Turtle.
Posts: 520
iTrader: (0)
sentythee is just really nicesentythee is just really nicesentythee is just really nicesentythee is just really nice
Guild: Titans
Default

Quote:
Originally Posted by TogSawks
lol...

i would say the bartender will never lose. So 0.

If you multiply infinite times of 1/2 probability you'll just get 0. I was never good at probabililty at school so thats just a guess xD
I DON'T understand, but it's impossible for the probability to be 0.
Law of large numbers: As the number of flips goes to infinity, the ratio of heads to tails will go to 1:1. Saying that the chance of getting a ratio of 1:2 at some point infinitely far away is 100% would contradict that law.

@Skillz: What would you say if the initial number of heads was 100? If the answer is 50% starting with 20 heads, it's impossible for the answer to be 50% with 100 heads.

Quote:
Originally Posted by Xpecial
However, I have not taken any statistics class, so if there is some weird solution, don't kill me for being wrong.
All you need is (love) algebra
__________________
 
11-14-2008   #6 (permalink)
k0n
YOUUUUUUUUUUUUUUUUUU
Special
k0n's Avatar
Games
Trickster OnlineGunboundAtlantica Online
Awards Retired Forum ModeratorEvent WinnerSotW MasterFacebook Fan
 
Join Date: Jun 2008
Location: Arasuka
Posts: 1,493
Blog Entries: 1
iTrader: (0)
k0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond reputek0n has a reputation beyond repute
Send a message via MSN to k0n
IGN: [JW]
Class: Hisui
Level: ****
Guild: YEAH
Default

Unless that coin is actually improportional due to weight balances, it's 50%.

Quote:
Originally Posted by sentythee
@Skillz: What would you say if the initial number of heads was 100? If the answer is 50% starting with 20 heads, it's impossible for the answer to be 50% with 100 heads.
Theory and reality are two different environments. Even though you may have a probability that situation B may occur with situation A, that doesn't mean that probability will account for what will happen.
__________________

Last edited by k0n; 11-14-2008 at 10:07 AM.
 
11-14-2008   #7 (permalink)
ggFTW Stalker
 
Join Date: Jul 2007
Location: In reckless abandon, I follow the Turtle.
Posts: 520
iTrader: (0)
sentythee is just really nicesentythee is just really nicesentythee is just really nicesentythee is just really nice
Guild: Titans
Default

Alright, I think I understand why people are saying 50%. And to clear that up:
Quote:
Originally Posted by sentythee
"You've flipped the coin 20 times landed heads every single time. Let's try something different for the next Double-or-Nothing. I'll let you keep flipping the coin as many times as you like. If at any point you have managed to land twice as many tails as you have landed heads, I'll call off all the money you owe me. The 20 you've already flipped will still count against you."
>>
__________________
 
11-14-2008   #8 (permalink)
<3
Vaizado's Avatar
Awards Event WinnerSotW Beginner
 
Join Date: Jun 2008
Posts: 844
Blog Entries: 1
iTrader: (0)
Vaizado will become famous soon enough
IGN: Vaiki
Default

So aren't we looking for a probability of landing the next 40 coins tails
__________________
 
11-14-2008   #9 (permalink)
ggFTW Stalker
 
Join Date: Jul 2007
Location: In reckless abandon, I follow the Turtle.
Posts: 520
iTrader: (0)
sentythee is just really nicesentythee is just really nicesentythee is just really nicesentythee is just really nice
Guild: Titans
Default

No, the bartender can also flip 5 heads and 50 tails to win (for a total of 25 heads and 50 tails). He can also flip 100 heads and 240 tails to win (120 heads, 240 tails total).
__________________
 
11-14-2008   #10 (permalink)
ggFTW Stalker
eD3N's Avatar
 
Join Date: Jun 2008
Posts: 577
iTrader: (0)
eD3N has a spectacular aura abouteD3N has a spectacular aura abouteD3N has a spectacular aura about
Send a message via MSN to eD3N
Default

Doesn't it multiply after every try?

Like so-
1st flip :
------------1/2% heads --- 1/2% tail
------------|---------------------|
2nd flip 1/2 and 1/2-----------1/2 and 1/2
---------|----------|------------|-----------|
3---1/2l 1/2---1/2--1/2-----1/2l1/2------1/2l1/2

so on and so on..

let's say for 3 heads in a row chances would be (1/2*1/2*1/2)= 0.125 or 12.5% chance
flipping heads 20 times = 0.0000009536743 or 0.00009536743% ( lol)

I dunno about the problem, I was just trying to remember how to do probability problems, it's been really long time :0

Also, the chance of him getting heads infinite times will never be 0%, there will always be a chance, even if it's incredibly small
 
11-14-2008   #11 (permalink)
ZeR
ggFTW Stalker
Special Games
La TaleDragon Nest
 
Join Date: Jun 2008
Location: Australia
Posts: 1,759
iTrader: (9)
ZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of light
Default

in relation to probability of 0, anything tending towards infinity can be 0 or a really large number.

1/infinity is infact 0
 
11-14-2008   #12 (permalink)
C.I.A. Rad Bromance
Torikakae's Avatar
Games
Trickster OnlineAuditionGrand ChasePangya
Awards Event WinnerMoM AwardWandering Eye
 
Join Date: Jun 2008
Location: In An Epic Battle
Posts: 5,216
Blog Entries: 17
iTrader: (12)
Torikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond reputeTorikakae has a reputation beyond repute
Send a message via MSN to Torikakae Send a message via Yahoo to Torikakae Send a message via Skype™ to Torikakae
IGN: Torikakae
Class: Buffalo to_buffalo
Level: 400
Guild: Mirage Coordinator
Default

I thought that infinity is not a number, therefore cannot be used in algebraic equations. So you can't divide by infinity, right?
 
11-14-2008   #13 (permalink)
Legends of League
Dragon's Avatar
Games
Trickster OnlineLeague of Legends
 
Join Date: Jun 2008
Location: Montreal
Posts: 2,622
iTrader: (60)
Dragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond repute
IGN: Ideality
Level: 30
Default

In limits, using infinity is allowed to determine end behaviour.
__________________


League of Legends Fanatic - NA - Ideality

 
11-14-2008   #14 (permalink)
ZeR
ggFTW Stalker
Special Games
La TaleDragon Nest
 
Join Date: Jun 2008
Location: Australia
Posts: 1,759
iTrader: (9)
ZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of light
Default

so i don't really see how you can use algebra to solve this.

all i can say is probability was bartender winning is 100% at infinity, unless the OP gives another logical solution.
 
11-14-2008   #15 (permalink)
Discuss.
Xpecial's Avatar
Games
League of LegendsAionAlliance of Valiant ArmsBloodline Champions
Awards Retired Forum ModeratorMoM Award
 
Join Date: Jun 2008
Location: California
Posts: 3,019
iTrader: (1)
Xpecial has disabled reputation
Send a message via AIM to Xpecial
IGN: Xpec
Class: Dainn lu_dainn
Level: -
Guild: -
Default

Well, obviously he doesn't just mean Algebra 1, or concepts specifically taught in those classes.

Probability is in Algebra btw.
__________________
 
11-14-2008   #16 (permalink)
Planeswalker
RoflKnife's Avatar
ggFTW Star
Games
ElswordDungeon Fighter OnlineDragon Nest
Awards Retired Content StaffEvent WinnerPervert Award
 
Join Date: Jul 2008
Posts: 3,987
iTrader: (0)
RoflKnife has disabled reputation
Default

._.

I'd say 100% due to luck? Since theres in a 50% chance of getting either heads or tails, you need to get lucky enough to get more tails than heads, so if you keep flipping EVENTUALLY you'll get 2:1?

If you want to be a realistic bastard though, just say the bartender will die before he can flip 2:1 since you'd have to flip that coin for an incredibly long time unless he has LUCK HAX.
__________________
 
11-14-2008   #17 (permalink)
ZeR
ggFTW Stalker
Special Games
La TaleDragon Nest
 
Join Date: Jun 2008
Location: Australia
Posts: 1,759
iTrader: (9)
ZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of light
Default

if LK doesnt work on trickster it won't work on maths either hahahaha.

Maths will always have some retarded solution to anything, so luck is out of the question. However, I can agree that if i was an realistic bastard, the bartender would have already died.
 
11-15-2008   #18 (permalink)
ggFTW Stalker
 
Join Date: Jul 2007
Location: In reckless abandon, I follow the Turtle.
Posts: 520
iTrader: (0)
sentythee is just really nicesentythee is just really nicesentythee is just really nicesentythee is just really nice
Guild: Titans
Default

I already posted why it was impossible for the answer to be 0%.
More in depth:
Assumptions: As the number of flips approaches infinite, the ratio of heads to tails will approach 1:1 (the law of large numbers says the the ratio of different outcomes will approach the ratio of the probability of each outcome as the number of outcomes approaches infinite).
The chance that the bartender loses is 0% for any initial number of heads (this is what you're saying)

k is the initial number of heads (in this problem, 20). I'm going to make k the variable here because, according to you, the bartender can't lose this bet regardless of what k is (as long as it's a positive integer).
As k approaches infinite, you're saying the the ratio of heads to tails at some point infinitely far away will be 2:1. This violates the law of large numbers, so one of the assumptions must be wrong.

Also, keep in mind that the chance of getting twice as many tails as heads decreases every time the bartender flips a head.

I'll give the answer to individual people, but I won't post it here.
__________________

Last edited by sentythee; 11-15-2008 at 10:52 AM.
 
11-15-2008   #19 (permalink)
ZeR
ggFTW Stalker
Special Games
La TaleDragon Nest
 
Join Date: Jun 2008
Location: Australia
Posts: 1,759
iTrader: (9)
ZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of lightZeR is a glorious beacon of light
Default

Law of large numbers what the hell?
 
11-15-2008   #20 (permalink)
Legends of League
Dragon's Avatar
Games
Trickster OnlineLeague of Legends
 
Join Date: Jun 2008
Location: Montreal
Posts: 2,622
iTrader: (60)
Dragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond reputeDragon has a reputation beyond repute
IGN: Ideality
Level: 30
Default

That's theory for you, the more you think about it, the more your head hurts.

Love these awesome Law names
__________________


League of Legends Fanatic - NA - Ideality

 

Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


zOMG!
Need a new browser game?

Try 

zOMG!

Rating:  

6.4
Hide this banner by registering for our community.