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.
The odds of 5 coming up are 1/99. So the odds of 5 not coming up, surprisingly, are 98/99.
ReplyDeleteWith 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?
ReplyDeleteFor 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.
ReplyDeleteIf 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!
ReplyDeleteThank 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.)
This comment has been removed by the author.
ReplyDeleteI knew I had screwed up! I bow to thee, whoever you are.
ReplyDeleteWitness the eggheads, I'm not ashamed of being confused on this one.
ReplyDeleteI love such mind benders, it's good food for my old brain.
ReplyDeleteI'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?
ReplyDeleteI 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.
ReplyDelete(To be frank, I'd no idea a 100-sided die existed.)
ReplyDeletehttp://en.wikipedia.org/wiki/Percentile_die
ReplyDeleteNow I think about it he had a D10 in 10's, not a true D100. I'd like one of those.