## Thursday, July 27, 2006

### What are the odds again?

The field of statistics owes a great deal of it's history to the human desire to gamble. At one point, a major contributor to statistics was interested in the following question:

What's the probability of rolling at least one six in four rolls of a die?

1. 51.774691358024691358...%

I won't spoil how I got it for someone else.

2. Let me see if I can get this one.

The odds of rolling at least one six should be the complement of the odds of rolling no sixes, i.e. 1 minus the odds of rolling no six.

The next issue is: what are the odds of rolling a six in a single roll?

Since each die has 6 possible outcomes, the odds of NOT rolling a 6 are 5/6. Therefore, the odds of NOT rolling a 6 in 4 consecutive rolls is (5/6)^4, which is 0.4823 or so.

Therefore, the odds of rolling at least one sex is 1 - 0.4825, or 0.5177, which is the number Abe came up with as well.

Another interesting question is the same one, except using two dice. In this case, the odds of rolling a 6 (total) on two dice is 5/36...because there are 36 combinations of the two dice, and a 6 can be rolled with (1,5) (5,1) (2,4) (4,2) or (3,3)....follow the logic above to calculate the final odds.

Mike--how many people read this blog each day?

3. It depends, but over the past week I had over 600 unique views (about 90 visitors a day), with over 900 page views. But most of that is search traffic.

If you want to know how many come by everyday, that's harder to figure out. I would guess at about 15 - 20 'loyal readers'.

BTW, I'm off tomorrow through the weekend, so I'll see you all on Monday!

4. nice little addition there, andy. yeah, that's the way I solved it. You could also solve it by adding up the probabilities of rolling one 6, two 6s, three 6s, and four 6s, which are:

one 6: (5/6)^3*(1/6)*4 (the "times four" accounts for different orders you could do it in)
two 6s: (5/6)^2*(1/6)^2*6
three 6s: (5/6)*(1/6)^3*4
four 6s: (1/6)^4

Add 'em up and you get the same answer. Hooray for math.

5. I made a funny typo in my original post if you go back and read it...

6. This comment has been removed by a blog administrator.

7. Haha, yeah, I caught that the first time, and I was going to make some snide remark, but I decided against it for some reason...

Would you roll a male or a female?

8. I shoulda kept my book on prob/stat

9. Sounds more like a genetic probability problem! ;-) I missed that the first time I read it.

I'd say Andy explained it better than I would have either way.

10. Which would you be more likely to deal more damage with on a critical hit?

A Greatsword or a Greataxe?

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