Perms and Combs! and some induction..

careless25 · 2011-05-29 21:08:12

Yea so my logic is that the first card will always be 100% correct, the next card has a probability of 36/51, and the third will be 22/50, but the fourth has to be the compliment so 42/49. Does that make sense?

bobbym · 2011-05-29 21:17:13

No, hold on one second. You have not given all the rules. What is a 3 card badugi?

careless25 · 2011-05-29 21:20:50

Ok so basically you are dealt 4 cards, out of the 4 cards, 3 of them have different suits and different values but the last one is either the same suit/value as one of the three. What are the odds of this?
I think you misread the question before.

bobbym · 2011-05-29 21:24:17

What about a 3 card badugi. Are you saying it does not matter if some of them are badugis?

careless25 · 2011-05-29 21:25:56

There is never a 3 card badugi, for a badugi you need 4 cards with 4 different suits and values.

careless25 · 2011-05-29 21:30:12

In other words, you are one card away from a Badugi. This is fairly tricky, so be careful with the counting here. The correct answer is between 55% and 60%.

bobbym · 2011-05-29 21:31:30

Okay, I will work on it and post when I have something.

careless25 · 2011-05-29 22:01:00

Hahaha I knew I was right about the balls and slots, I was just mixing up the variables

Where n is the number of letters and k is the number of slots. We learned the right side of the equation in class so I am more accustomed to that, I just have to figure out which variable is which.

gAr · 2011-05-29 23:08:37

Hi all,

Let me check whether I understood it correct.

First, I'll calculate the number of ways to get a badugi:

52*38*24*10 ways
Do we agree?

bobbym · 2011-05-29 23:25:36

Hi gAr;

That is a little off.

gAr · 2011-05-29 23:28:30

Hmmm, what went wrong?

bobbym · 2011-05-29 23:31:34

Hi;

It is very difficult to do it that way. I always seem to leave someone out. The right answer I think is 52 * 36 * 22 * 10 another way
is

gAr · 2011-05-29 23:43:57

Hi,

I don't understand.
First card can be any: 52
Second card the different suit, and different value: 52 - 13 -1 = 38
Third : 52 - 26 - 2 = 24
Fourth : 52 - 39 - 3 = 10

Something wrong here?

careless25 · 2011-05-29 23:50:05

Hi gAr!

Its actually
second card: different sut different VALUE so 52 - 13 - 3 = 36
third card: 52-26 - 4 = 22

Last edited by careless25 (2011-05-29 23:51:35)

careless25 · 2011-05-29 23:54:10

AHHH!! HAHAHA Bobbym i am pretty sure that is not the right answer....remember the hint: it is between 55% and 60%...ur answer is 6.3%

bobbym · 2011-05-29 23:55:11

What answer, I have no answer so far.

careless25 · 2011-05-29 23:58:55

Oh! I thot

was wat your answer was.
Nvm that is actually correct and agrees with my answer for the probability of getting a badugi.

bobbym · 2011-05-30 00:01:56

Yes, that is for a badugi. I was just showing a simpler way for gAr.

How do you know the 3 card problem is 55% - 60%?

careless25 · 2011-05-30 00:12:34

That was stated in the question. (I did not post it when i posted the question)

careless25 · 2011-05-30 01:20:49

3 cases:
1. diff value, same suit as one card

2. diff suit, same value as one card
3. same suit, same value with another card

Final answer:

make sense???

gAr · 2011-05-30 01:24:54

Hi all,

The answer I get is :
52*36*24*39 / (52*51*50*49)

I get the same by direct counting also.

gAr · 2011-05-30 01:54:02

Hi,

We can consider only 2 cases:
1)
Fourth card is of one of the suites already there:
52*36*24* (36)

2)
Fourth card is of the other remaining suit:
52*36*24* (3)

Hence 1) + 2) = 52*36*24* (36+3) ways

bobbym · 2011-05-30 05:11:54

Hi;

That is what I got but he said it was between 55% and 60% which I do not yet understand.

gAr · 2011-05-30 05:20:11

Hi bobbym,

Since computer too verifies it, I guess 55-60% must be a mistake, or the question is incomplete.

bobbym · 2011-05-30 05:31:19

That is what I was thinking.

Math Is Fun Forum

#26 2011-05-29 21:08:12

Re: Perms and Combs! and some induction..

#27 2011-05-29 21:17:13

Re: Perms and Combs! and some induction..

#28 2011-05-29 21:20:50

Re: Perms and Combs! and some induction..

#29 2011-05-29 21:24:17

Re: Perms and Combs! and some induction..

#30 2011-05-29 21:25:56

Re: Perms and Combs! and some induction..

#31 2011-05-29 21:30:12

Re: Perms and Combs! and some induction..

#32 2011-05-29 21:31:30

Re: Perms and Combs! and some induction..

#33 2011-05-29 22:01:00

Re: Perms and Combs! and some induction..

#34 2011-05-29 23:08:37

Re: Perms and Combs! and some induction..

#35 2011-05-29 23:25:36

Re: Perms and Combs! and some induction..

#36 2011-05-29 23:28:30

Re: Perms and Combs! and some induction..

#37 2011-05-29 23:31:34

Re: Perms and Combs! and some induction..

#38 2011-05-29 23:43:57

Re: Perms and Combs! and some induction..

#39 2011-05-29 23:50:05

Re: Perms and Combs! and some induction..

#40 2011-05-29 23:54:10

Re: Perms and Combs! and some induction..

#41 2011-05-29 23:55:11

Re: Perms and Combs! and some induction..

#42 2011-05-29 23:58:55

Re: Perms and Combs! and some induction..

#43 2011-05-30 00:01:56

Re: Perms and Combs! and some induction..

#44 2011-05-30 00:12:34

Re: Perms and Combs! and some induction..

#45 2011-05-30 01:20:49

Re: Perms and Combs! and some induction..

#46 2011-05-30 01:24:54

Re: Perms and Combs! and some induction..

#47 2011-05-30 01:54:02

Re: Perms and Combs! and some induction..

#48 2011-05-30 05:11:54

Re: Perms and Combs! and some induction..

#49 2011-05-30 05:20:11

Re: Perms and Combs! and some induction..

#50 2011-05-30 05:31:19

Re: Perms and Combs! and some induction..

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