Basic probability

[thirtythree]

My philosophy textbook presents these figures and says to figure out how to reach the given solutions for extra practice. I can do some, but I can't find any consistent method that works for all of them. I've looked all over this rather small section of the textbook and, as far as I can tell, it doesn't tell us how to do them.

When throwing 5 dice:
1. The probability of getting no two alike = .0926
2. The probability of getting one pair = .4630
3. The probability of getting two pair = .2315
4. The probability of getting three alike = .1543
5. The probability of getting a full house = .0386
6. The probability of getting four alike = .0193
7. The probability of getting five alike=.0008

UPDATE:

Okay, I think I've got all of them except for 3, though I could still be doing them wrong. I'm not entirely sure why I'm doing 5cX. It seems to work if I do 5c[# of die alike], but if that's the rule, why with the full house, for example, isn't it 5c3*5c2? 😕

7776 = 6^5 (the total number of possible rolls)

1. 6*5*4*3*2/7776 = .0926
2. 6*1*5*4*3*5c2/7776 = .4630
3. 6*1*5*1*4*???/7776 = .2315 - 6c2 works in place of the ???, but I'm not sure why I'd do that, and I'm sure there are a number of ways I could get 15
4. 6*1*1*5*4*5c3/7776 = .1543
5. 6*1*5*1*1*5c3/7776 = .0386
6. 6*1*1*1*5*5c4/7776 = .0193
7. 6*1*1*1*1/7776 = .0008

 

[Bootprint]

It's philosophy book, they probably just make up the numbers.

 

[thirtythree]

Oops, guess I should explain the rules of the game.

The game of poker dice is played with 5 dice which are thrown
simultaneously.

 

[thirtythree]

*cough*

 

[thirtythree]

Last try. Any late night probability geniuses?

 

[HaxorNubcake]

isn't this just binomial distribution?

edit: wait thats just a big maybe...not thinkin clearly right now.

edit: but yeah, these are really simple. I'll figure it out in a few minutes (maybe)

 

[thirtythree]

Originally posted by: HaxorNubcake
isn't this just binomial distribution?

edit: wait thats just a big maybe...not thinkin clearly right now.

edit: but yeah, these are really simple. I'll figure it out in a few minutes (maybe)

I thought binomial distributions were just success/fail sorta things. Like... not dice.

 

[HaxorNubcake]

edit: forget it. i'll do it in the morning

 

[Fenixgoon]

those are wrong.. at least 7, which is the easiest to test.. 1/6 ^5 = 0.0001286

GG philosophy

 

[olds]

50/50

 

[dighn]

Originally posted by: Fenixgoon
those are wrong.. at least 7, which is the easiest to test.. 1/6 ^5 = 0.0001286

GG philosophy

but there are 6 choices!

(1/6&5)*6 = 0.0007716

GG

 

[thirtythree]

Originally posted by: Fenixgoon
those are wrong.. at least 7, which is the easiest to test.. 1/6 ^5 = 0.0001286

GG philosophy

Naw, it's that times 6. It doesn't matter what the first roll is. EDIT: beat me to it

 

[HaxorNubcake]

Originally posted by: thirtythree

Originally posted by: HaxorNubcake
isn't this just binomial distribution?

edit: wait thats just a big maybe...not thinkin clearly right now.

edit: but yeah, these are really simple. I'll figure it out in a few minutes (maybe)

I thought binomial distributions were just success/fail sorta things. Like... not dice.

IIRC binomial distributions simply means that each possible outcome has an equal chance

 

[Fenixgoon]

Originally posted by: dighn

Originally posted by: Fenixgoon
those are wrong.. at least 7, which is the easiest to test.. 1/6 ^5 = 0.0001286

GG philosophy

but there are 6 choices!

(1/6&5)*6 = 0.0007716

GG

fair enough.. but its still not 0.0008 😀

 

[HaxorNubcake]

for these problems, is it the probability of getting AT LEAST x number the same, or exactly x number the same. it makes a difference

 

[chuckywang]

For some of them, it'll be easier to find the probability of the negation.

 

[HaxorNubcake]

goddamnit this stuff is so basic...yet i can't figure it out anymore. 🙁

edit: and since it's philosophy...are you sure that these are 6 sided dice? 😀

 

[sygyzy]

I don't think the numbers are correct. Are you positive of these answers?

 

[chuckywang]

I'll do the first one: the probability of getting no two alike.

Consider the first dice. It could be one of six numbers. The probability of the second dice being a different number is 5/6. The probability of the third dice being different than the first two is 4/6. The probability of the fourth dice being different than the first three is 3/6. The probability of the fifth dice being different than the first four is 2/6. Therefore the total probability is 5/6*4/6*3/6*2/6 which is about .0926.

 

[Yossarian]

YAHTZEE!!!

 

[chuckywang]

Originally posted by: sygyzy
I don't think the numbers are correct. Are you positive of these answers?

I checked the first two, and they are correct.

 

[thirtythree]

Originally posted by: HaxorNubcake
for these problems, is it the probability of getting AT LEAST x number the same, or exactly x number the same. it makes a difference

I believe it's exactly, because the numbers all add up to 1.

 

[chuckywang]

Yep, all five values are correct.

 

[thirtythree]

Okay, I think I've got all of them except for 3, though I could still be doing them wrong. I'm not entirely sure why I'm doing 5cX. It seems to work if I do 5c[# of die alike], but if that's the rule, why with the full house, for example, isn't it 5c3*5c2? 😕

7776 = 6^5 (the total number of possible rolls)

1. 6*5*4*3*2/7776 = .0926
2. 6*1*5*4*3*5c2/7776 = .4630
3. 6*1*5*1*4*???/7776 = .2315 - 6c2 works in place of the ???, but I'm not sure why I'd do that, and I'm sure there are a number of ways I could get 15
4. 6*1*1*5*4*5c3/7776 = .1543
5. 6*1*5*1*1*5c3/7776 = .0386
6. 6*1*1*1*5*5c4/7776 = .0193
7. 6*1*1*1*1/7776 = .0008