If you cast a 99-sided die 99 times, what are the odds of number 5 not coming up?
And for a 9-sided die cast nine times? And a 999-sided die cast 999 times?
This is not a riddle, I just want to know.
Anon informed:
If you cast a 99-sided die once, the probability of 5 not coming up is 98/99. If you cast a 99-sided die twice, the probability of 5 not coming up either time is (98/99) * (98/99). So, the odds of the number 5 not turning up after 99 throws is 98/99 multiplied by itself 99 times. This works out at about 0.366.
For a 9-sided die, it works out at about 0.346, and for a 999-sided die, about 0.368.
It's related to the mathematical number 'e'. As the number of faces increases, the probability gets closer and closer to 1/e.
eolake:
Yes!
Thank you.
I had an intuitive feeling the number would be about the same, but I couldn't get my head around the math. (School is thirty years ago after all, and I don't think we ever got into probabilities.)
I also felt that the number was not all that small. 0.37 sounds about right.
12 comments:
The odds of 5 coming up are 1/99. So the odds of 5 not coming up, surprisingly, are 98/99.
With a 9 sided die, that would be 1/9 and 8/9 respectively.
And 1/999 & 998/999 as well.
If you cast a 99-sided die 99 times, what are the odds of number 5 not coming up?
For a single cast the odds of any one number coming up is 1/99. The odds of it not coming up is therefore 98/99. The odds for a repeated cast are the same. When multiple repeated casts are taken together, just multiply: 99 * (1/99) = .99. Therefore, the odds of it not coming up when cast 99 times are 0.01.
Sorry guys, you're both wrong.
If you cast a 99-sided die once, the probability of 5 not coming up is 98/99. If you cast a 99-sided die twice, the probability of 5 not coming up either time is (98/99) * (98/99). So, the odds of the number 5 not turning up after 99 throws is 98/99 multiplied by itself 99 times. This works out at about 0.366.
For a 9-sided die, it works out at about 0.346, and for a 999-sided die, about 0.368.
It's related to the mathematical number 'e' (see Wikipedia). As the number of faces increases, the probability gets closer and closer to 1/e.
Yes!
Thank you.
I had an intuitive feeling the number would be about the same, but I couldn't get my head around the math. (School is thirty years ago after all, and I don't think we ever got into probabilities.)
I knew I had screwed up! I bow to thee, whoever you are.
Witness the eggheads, I'm not ashamed of being confused on this one.
I love such mind benders, it's good food for my old brain.
I'm a loser type of guy when it comes to mathematics, though.
Yet I love the formality, the beauty of figures and formulas.
I'd like to know what world you live in EO?
I have a small bag of dice, and in it I have D4,D6, D8, D10 and D20. I've had gamer friends who had D100's.
I don't think I've seen a D9 or a D99.
My D999 is a heck of a thing to behold.
(To be frank, I'd no idea a 100-sided die existed.)
http://en.wikipedia.org/wiki/Percentile_die
Now I think about it he had a D10 in 10's, not a true D100. I'd like one of those.
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