tag:blogger.com,1999:blog-4891509519427970698.post8697545572021591051..comments2024-01-06T04:13:41.492-07:00Comments on A Paladin In Citadel: A Math ProblemAaron E. Steelehttp://www.blogger.com/profile/07789462075611254929noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4891509519427970698.post-23975060924782149532010-04-02T23:41:47.538-06:002010-04-02T23:41:47.538-06:00The probability for k successes rolling n dice is
...The probability for k successes rolling n dice is<br /><br />n! / (k!((n-k)!)) p^k q^{n-k}<br /><br />Where p=1/6 is the probability of success and q=1-p=5/6 is the probability of failure.Liorhttps://www.blogger.com/profile/15563497907340566955noreply@blogger.comtag:blogger.com,1999:blog-4891509519427970698.post-89638222586338782512010-03-23T00:40:50.174-06:002010-03-23T00:40:50.174-06:00Incidentally, looking at my notes, your calcs shou...Incidentally, looking at my notes, your calcs should be very accurate up to 7 dice. Would you believe their are 1,679,616 combinations with 8 dice, over 10 million with 9 dice, at over 60 million with 10 dice? Try figuring those probabilities manually!Aaron E. Steelehttps://www.blogger.com/profile/07789462075611254929noreply@blogger.comtag:blogger.com,1999:blog-4891509519427970698.post-73010614772149804852010-03-23T00:37:36.272-06:002010-03-23T00:37:36.272-06:00You are a scholar and a gentleman!
My most sincer...You are a scholar and a gentleman!<br /><br />My most sincere thanks, my wife will be pleased that I will stop mumbling "factorials, factorials!" in my sleep.Aaron E. Steelehttps://www.blogger.com/profile/07789462075611254929noreply@blogger.comtag:blogger.com,1999:blog-4891509519427970698.post-8328107159961664682010-03-23T00:31:57.592-06:002010-03-23T00:31:57.592-06:00Sorry, no remember math neither. Instead I have p...Sorry, no remember math neither. Instead I have puter brute force. 10min and 1,000,000 rolls per row later we get some sadly not very accurate data. Who cares about tenths of a percentage anyway?<br /><br />Oh why is the pre tag not allowed, curse you formating heathans!<br /><br />| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |<br />| 1 | 83.34 | 16.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 2 | 69.48 | 27.75 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 3 | 57.87 | 34.76 | 6.91 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 4 | 48.17 | 38.64 | 11.59 | 1.54 | 0.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 5 | 40.21 | 40.15 | 16.07 | 3.23 | 0.32 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 6 | 33.46 | 40.21 | 20.15 | 5.33 | 0.79 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 7 | 27.99 | 39.04 | 23.39 | 7.83 | 1.55 | 0.18 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 8 | 23.24 | 37.29 | 26.01 | 10.41 | 2.59 | 0.42 | 0.04 | 0.00 | 0.00 | 0.00 | 0.00 |<br />| 9 | 19.32 | 34.93 | 27.96 | 13.00 | 3.91 | 0.77 | 0.10 | 0.01 | 0.00 | 0.00 | 0.00 |<br />| 10 | 16.11 | 32.28 | 29.08 | 15.60 | 5.41 | 1.30 | 0.22 | 0.03 | 0.00 | 0.00 | 0.00 |Norman J. Harman Jr.https://www.blogger.com/profile/01319655075997712313noreply@blogger.com