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Unregistered
08-20-2002, 06:45 PM
I have one simple question for you guys to answer:

Five hats are randomly distributed to the five people who own them. What is the probability that all the poeple receive the correct hat?

Good Luck

Sentaku senshi
08-20-2002, 06:51 PM
1 in 25.

What is the chance that was a homework queston?

ygfperson
08-20-2002, 06:53 PM
1/5! = 1 in 120

a person takes a hat. s/he has a 1 in 5 chance. if the choice is correct, the next person has a 1 in 4 chance, then a 1 in 3 chance ,and so on.

i'm sure i'm wrong... am i?

MrWizard
08-20-2002, 07:07 PM
Originally posted by ygfperson
1/5! = 1 in 120

a person takes a hat. s/he has a 1 in 5 chance. if the choice is correct, the next person has a 1 in 4 chance, then a 1 in 3 chance ,and so on.

i'm sure i'm wrong... am i?

That's my answer also, I believe it to be correct.

Sentaku senshi
08-20-2002, 07:09 PM
Each person has a 1 in 5 chance of getting the correct hat. YGF your method would have worked if the queston said that No more hats would be given out once someone got the wrong hat. But everyone gets a hat no mater what.

dirkduck
08-20-2002, 07:15 PM
That would just be a 5^2 one I believe...so 1 in 25 (as stated before ;))

moi
08-20-2002, 07:15 PM
1 in 3125

ygfperson
08-20-2002, 07:16 PM
Originally posted by Sentaku senshi
Each person has a 1 in 5 chance of getting the correct hat. YGF your method would have worked if the queston said that No more hats would be given out once someone got the wrong hat. But everyone gets a hat no mater what.
oh yeah... forgot about that. see what school does to you? :D

Aran
08-20-2002, 07:47 PM
the law of permutations is in effect here.. i believe it states that (n)/((n-k)!) is the answer (where k is accepted and n are the total number of outcomes)

[it's either (n)/((n-k)!) or (n!)/((n-k)!)]

Prelude
08-20-2002, 07:54 PM
>Five hats are randomly distributed to the five people who own them.
According to your wording, all five people own all five hats, so the probability is 1 in 1.

-Prelude

darkeldar77
08-20-2002, 08:07 PM
Another for 1/120

Brian
08-20-2002, 08:08 PM
I envy the one with the red hat (http://www.redhat.com)

Terrance
08-20-2002, 08:31 PM
1/120

:o

DavidP
08-20-2002, 08:34 PM
i get 1/120 also..

I envy the one with the red hat

hahahahaha

Jet_Master
08-20-2002, 08:42 PM
I very much believe it is a 1 in 25 chance...
because each hat has a chance of landing on one of five people (that is a 1 in 5 chance). but when there are five hats, the chances are multiplied by another 1 in 5 chance. therefore:
1/5 * 1/5 = 1/25.
therefore there is a 1 in 25 chance everyone will get the right hat...

Jet_Master
08-20-2002, 08:45 PM
WTF is happening????? I did sign in. how come it is showing me as a guest???? I know i am a member of this board!!
Help me moderator (or somebody)

Eibro
08-20-2002, 08:48 PM
You have to use the user cp if you want to sign in (well most people do...)

According to your wording, all five people own all five hats, so the probability is 1 in 1.
I'd have to go with that answer aswell.

moonwalker
08-20-2002, 09:06 PM
First, let's see ...

Probability = (Favourable Outcomes) / (Total Number of outcomes)

Favourable Outcomes....

it's when all the five have their own
hats... no other combination is acceptable... so only 1 favourable
outcome

Total Outcomes ....

Five hats can be given to 5 people in 5! ways

5! = 5 * 4 * 3 * 2 * 1 = 120

Probability (P) = 1/120

Have fun :)

moonwalker
08-20-2002, 09:10 PM
now you ask me why 5! ways ?

observe the pattern carefully... if you can follow
till 3, you'll understand...

1 person ... 1 hat ... 1 way ... ( 1! )

2 persons .. 2 hats ... 2 ways ... ( 2! )

3 persons ... 3 hats ... 6 ways ... ( 3! )

4 persons ... 4 hats ... 24 ways ... ( 4! )

5 persons ... 5 hats ... 120 ways .... ( 5! )

from the above pattern,

n persons ... n hats ... n! ways

moonwalker
08-20-2002, 09:26 PM
here's another way of looking at it (if you're still interested)

5 hats - 1 2 3 4 5
5 girls :D - A B C D E

probability of A getting the right hat (out of 5 hats)

1/5

probability of B getting the right hat (out of remaining 4 hats)

1/4

probability of C getting the right hat (out of remaining 3 hats)

1/3

probability of D getting the right hat (out of remaining 2 hats)

1/2

probability of E getting the right hat (out of remaining 1 hat)

1/1

Now if A gets the right hat, no one else gets A hat (sounds
dumb, but see...) ... it's the same for B C D & E

so these "events" tell us that it is conditional probability.
so, the probability of everybody getting their own hats is

1/5 * 1/4 * 1/3 * 1/2 * 1/1 = 1/5!

someone here said 1/3125

that answer will be correct if the person "picks" the right hat
and puts it back again ... and the rest do the same ("pick" the
right hat and put it back again)

Math is fun :)

Cshot
08-20-2002, 10:07 PM
1/5! = 1/120
Simple stats question.

DISGUISED
08-20-2002, 10:14 PM
1/5 * 1/4 * 1/3 * 1/2 * 1/1 = 1/5!

Ditto

BMJ
08-20-2002, 10:20 PM
:D

Odds of contracting and being affected by the West Nile virus in Illinois: 1/30000

DISGUISED
08-20-2002, 10:29 PM
Originally posted by BMJ
:D

Odds of contracting and being affected by the West Nile virus in Illinois: 1/30000

7 more cases found today, one critical, lucky us.

BMJ
08-20-2002, 10:48 PM
meh? Oh... yea, heh; Lucky :)

I just saw a bunch of stats, so I just felt like posting something :p

DISGUISED
08-20-2002, 10:50 PM
I am just glad I live downtown..I don't see to many bugs here.

MrWizard
08-20-2002, 11:41 PM
Okay , early i said 1/120 , I am sticking with that answer. Here is a little reasoning. Lets assume you have 5 objects. There are only a certain number of permuations for this set. 2 Permuations are

1,2,3,4,5
1,2,3,5,4

Just for example. To get the total number of permuations you do 5! which equals 120. Only 1 of those is right however because each of the 5 owners only owns 1 hat. So 1/120 is the correct answer. It doesn't matter if you pass out the hats all at once OR one by one, the answer holds.

Troll_King
08-21-2002, 05:09 AM
Is it a permutations answer or a combinations answer? I don't want to think about, but my guess after reading was 5! or 1 in 120 that each individual would recieve their own hat.

moonwalker
08-21-2002, 09:11 AM
probabilities are usually based on permutations.

combinations come into place when it doesn't matter
which way you give the hat as long as they get hats..

Eg.
The number of combinations of 3 girls :D sitting together in
3 seats is 1.
(doesn't care about arrangements.. as long as they sit
together, it's a combination.. different ways of arrangements
of the same are considered as repitition)

The number of permutations of 3 girls sitting together
in 3 seats is 6.
(does care about arrangements)

Now why would we want to study combinations then?
It's when we want to cancel out repititions.

For example, the number of ways of "choosing" 3 girls
from 12 girls is 12 C 3 (doesnt matter which way you
choose the girls, as long as you choose 3 of them)

The number of ways of "arranging" 3 specific girls out
of 12 is 12 P 3 (it matters which spice girl you pulled out
1st, 2nd and 3rd ;) )

Unregistered
08-21-2002, 11:03 AM
Most of you put what was expected: 1/25.
But the correct answer is: 1/120.

Thanks Again