Frank Morgan's Math Chat
May 2, 2002
GOODBYE. I have decided to retire my Math Chat column, after 142 appearances here and in The Christian Science Monitor. I would like to thank the Math Chat staff, my editors, contributors, and readers, who I trust will continue to find ways to tell the world that mathematics can be interesting and fun.
OLD CHALLENGE. (Jeff Repka). A sponsor of the Chicago Cubs radio broadcasts will attempt to give away a million dollars this season during each game. Before each game, a fan is selected from a random drawing of entries. Also, a position (excluding pitcher) is selected at random. If the Cubs player who starts the game at that position hits a grand slam in the seventh inning, the fan wins the million. If any other Cubs player hits a grand slam in the seventh inning, the fan wins ten thousand dollars. How safe is the sponsor's money?
ANSWER. Joe DeVincentis puts the expected cost at about $53,000. He expects four grand slams (like last season), a 1/9 chance it's by the selected player, and a 1/9 chance it's in the seventh inning, for an expectation from a $1,000,000 payout of
4 (1/9) (1/9) 1000000 ~ $49,000.
The 8/9 chance it's by another player gives an expectation from a $10,000 payout of
4 (8/9) (1/9) 10000 ~ $4,000,
for a total of $53,000. He figures that the smaller chance of a grand slam by the pitcher (there were no home runs by Cubs pitchers last year and only 29 out of about 3000 in the whole league) is compensated for by the chance of a grand slam by a mid-game replacement or designated hitter.
Jonathan Falk estimates that the chance of no payout is about 64% and that the chance of no $1,000,000 payout is about 95%. He computes these (using the Poisson distribution) as e-4(1/9) ~ 64% and e-4(1/9)(1/9) ~ 95%.
BALAKRISHNAN WINS HIGH SCHOOL CALCULUS AWARD. Jennifer Balakrishnan of Harvest Christian Academy in Barrigada, Guam has been awarded the second $1000 National High School Calculus Student Award, partly for a science fair project on elliptical coordinate systems. The runners up are Zachary John Abernathy (West Forsyth High School, Clemmons, NC), Brandon Batista (Monmouth Regional High School, Tinton Falls, NJ), Siva Kalyan (Littlebrook Elementary School, Princeton, NJ), and April Tam (Miami Springs Senior High School, Miami Springs, FL). For more information, see calculus.org.
QUESTIONABLE MATHEMATICS. Todd Feitelson of Millbrook School found this boner in a program for the NCTM's Canadian Regional Conference of the National Council of Teachers of Mathematics (NCTM):
"The Canadian dollar is roughly equivalent to $1.50 in U.S. funds."
Todd continues: This is backwards, of course, and some may say it is a typo (or Canadian optimism), but we math teachers know that it's a matter of reversed ratios.
Copyright 2002, Frank Morgan.
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