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Archeological evidence indicates that the ancient (pre-Roman) Etruscans played dice using a dodecahedral die having 12 pentagonal faces numbered 1 through 12 (figure above). One could simulate such a die by drawing a random card from a deck of cards numbered 1 through k. for your own personal value of k, begin with the largest digit in the sum of the digits in your student ID number. This is your value of k unless this digit is less than 5, in which case subtract it from 10 to get your own value of k. a.) John and Mary draw alternately from a deck of shuffled k cards. The first one to draw an ace-the card numbered one- wins. Assume that John draws first. Use the formula for the sum of a geometric series to calculate (both a rational number and a four place decimal) the probability J that John wins, and the probability M that Mary wins. Check that M+J=1. b.) Now John , Mary, Paul draw alternately from a deck of k cards. Calculate separately their respective probabilities of winning, given that John draws first and Mary draw second. Check that J+M+P=1.

My student no is 10-0244 in that case my largest digit is 4 so I subtracted it from 10 and I get the difference of 6 then k=6.

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    I'm probably being dense, but what does this have to do with either geometric series or differential geometry?2012-12-28
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    Dear Jhanette, telling the moderators `"needed to submit in january.. please help"` is not an appropriate use of a moderator flag.2012-12-28
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    Are the draws with or without replacement? (That is, if a player doesn't draw the ace, does he put his card back and reshuffle?) (The reference to geometric series suggests it's with replacement, as does the dice analogy.)2012-12-28
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    The sum of the digits of your student number is 11, and its largest digit is 1, so you should actually solve it for k=9.2012-12-28
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    thank you for answering my question. you gave me a big favor. :)2013-08-05

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