Probability Question

[TontoKowalski]

yeah if you had to specifically roll five "4's" then yes it would be 1/6 to the 5th not 4th, you are correct

this bar i used to live by had thsi game... for a dollar you got a roll and could win the pot if yo udid it (they limited you to 3 rolls per day)... i figured out that 1/6 to the 4th was 1/1296, so once there was approx $1300 in the pot, it was worth playing. MANY people were makin the mistake that it was 1/6th to the 5th odds of winning, which is about 1 in over 7k... which is not true

 

[jr11]

I started out as a Math Major before switching to Chemistry/Biology, but Proability of Statistics was by far the hardest class I ever took, that and Organic Chemistry. Haven't done this shit in about 15 years now, and yes it's gone.

 

[Agent 0659]

Where is Marine when you actually need him for once?

 

[marine]

I'm right here agent.
no reason for me to provide my hefty intelect here. You girls have things covered.

 

[TontoKowalski]

now here's a real brain cramper... if you roll 5 dice, what are the odds of 4 being the same?

well, its definitely still 6/6 for the "first" roll

but the 2nd roll can be either the number of the first or a new number.

the 3rd must be one of the first two rolls

the 4th must match the 3rd

the 5th must match the 4th

now the only problem is, I don't know how to compute this because if the 2nd roll matches the first, it changes the odds as opposed to rolling 2 different numbers on the first 2 rolls

assuming the first 2 rolls are different, it would be 1/3*1/6*1/6 = 1/108, so one out of every 108 rolls would yield 4 of a kind.

however, if the first two rolls are identical, then the remaining 3 would be ... well I don't know because you'd have 3 rolls to get 2 of the same number

 

[KotysDad]

now here's a real brain cramper... if you roll 5 dice, what are the odds of 4 being the same?

150/7776.


7776 is total number of possible rolls of 5 dice.

150 is gotten by....5x6x5

You got 5 dice, 4 sames and 1 different. That 1 different can be any one of 5 dice....hence the 5.

The four same dice can be any one of 6 values...hence the 6.

The dice thats different can be any of the other five numbers not on the sames....hence the 5.

 

[IntenseOperator]

150/7776.


7776 is total number of possible rolls of 5 dice.

150 is gotten by....5x6x5

You got 5 dice, 4 sames and 1 different. That 1 different can be any one of 5 dice....hence the 5.

The four same dice can be any one of 6 values...hence the 6.

The dice thats different can be any of the other five numbers not on the sames....hence the 5.

show off

 

[KotysDad]

lol...no, show-off would have been if I had added that this wasnt so much of a brain cramper as much as just someone asking the hamster to start walking on the wheel for a few minutes.

 

[TontoKowalski]

show off

I don't think you are correct. I don't think the odds of rolling 4 dice of the same number out of 5 is only 1.9% which is what 150 out of hte 7k number you had equates to.

 

[KotysDad]

I don't think you are correct.

:mj07:

Do you need the proof???

 

[justin22g]

:mj07:

Do you need the proof???

scan your sheet of paper where you worked the problem and post it :shrug:

 

[KotysDad]

scan your sheet of paper where you worked the problem and post it :shrug:

What paper?? lol 5x6x5 didnt need paper.

But I'll give the proof anyway.

Tonto is looking for dice of the pattern

s s s s d

That "d" can come in any one of 5 slots, namely

ssssd
sssds
ssdss
sdsss
dssss

Those "s" since they are alll the same can be any one of 6 numbers.....that gives us 5X6 so far.

That leaves picking the possilbilities for the "d". Since we already picked the "s", that leaves 5 possible choices left for the "d".

5X6X5 = 150

 

[marine]

I don't think you are correct. I don't think the odds of rolling 4 dice of the same number out of 5 is only 1.9% which is what 150 out of hte 7k number you had equates to.

http://joseph-bartlo.net/any-yahtzee.htm

5 dice rolled, 7776 possibilities:

None of the same dice : 720
Pair : 5400
3 of-a-kind : 1500
4 of-a-kind : 150
Yahtzee : 6

 

[TontoKowalski]

yeah, thats right... just seemed to occur more than 1.9%, we used to see people roll 4 but not 5 of the same all the time, it seemed