Challenge 5 Super Bowl Supposition PLEASE DO NOT RESPOND UNTIL 2/6/2012 12
am EST
As the Super Bowl approaches, suppose it will be decided like baseball. Four
of seven games determines a winner. Also suppose that the NFL has won the
first game.
Simulate results of 2000000 series and provide the number of times the NFL
wins in 4 5 6 7 games. If the AFL wins this Extended Super Bowl
Contest, the result is an 8 . Create a 2000000 item list of number of
games necessary to determine a winner and provide a frequency distribution.
fd=: [: /:~ ({. , #)/.~
fd (expression for 2000000 trials)
4 249561
5 374865
6 373851
7 312603
8 689120
]games=:fd n,.2000000$6
4 249301
5 376266
6 375281
7 311189
8 687963
]prob=:(4+i.5),. (1{"1 games)%2000000
4 0.124651
5 0.188133
6 0.18764
7 0.155595
8 0.343982
]+/(1{"1 games)%2000000
1
Now, confirm that your results are reasonable with a theoretical argument.
Also, enjoy the Super Bowl!
Linda
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