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  CMPU-145, Spring 2013
  Asmt. 6
  Solutions!
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  1:  Rolling 5 dice and getting exactly two pair!
------------------------

*num-ways-of-getting-2-pair* ====> 1800
*num-ways-of-rolling-5-dice* ====> 7776
*prob-getting-2-pair-in-5-dice* ====> 0.23148148148148148

(roll-5-dice) ====> (1 3 1 2 3)
(roll-5-dice) ====> (2 1 3 5 4)
(roll-5-dice) ====> (5 6 6 2 6)

(has-2-pair? '(1 2 3 2 1)) ====> #t
(has-2-pair? '(2 2 3 3 4)) ====> #t
(has-2-pair? '(5 2 3 4 3)) ====> #f

(gen-and-test 100000 roll-5-dice has-2-pair?) ====> 0.23048

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  2:  Powerball Expected Winnings
------------------------

*num-pb-tix* ====> 175223510
*pb-payoffs* ==>
200000000
1000000
10000
100
100
7
7
4
4

*pb-num-outcomes* ==>
1
34
270
9180
14310
486540
248040
1581255
3162510

*pb-probabilities* ==>
5.706996738051874e-09
1.9403788909376374e-07
1.540889119274006e-06
5.2390230055316206e-05
8.166712332152232e-05
0.002776682192931759
0.001415563470906387
0.009024217127028217
0.018048434254056434

*pb-odds* ==>
175223510.0
5153633.0
648976.0
19088.0
12245.0
360.0
706.0
111.0
55.0

*pb-exp-winnings* ====> 1.5018881884057682
*pb-exp-winnings-no-grand-prize* ====> 0.3604888407953933
*pb-no-winnings* ====> 0.9685993049676953

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  3:  Estimating Expected Winnings in Powerball
------------------------

(estimate-pb-exp-winnings 1000) ====> 0.193
(estimate-pb-exp-winnings 1000) ====> 0.249
(estimate-pb-exp-winnings 1000) ====> 0.181
(estimate-pb-exp-winnings 1000) ====> 0.169
(estimate-pb-exp-winnings 100000) ====> 0.18921
(estimate-pb-exp-winnings 100000) ====> 0.18206
(estimate-pb-exp-winnings 1000000) ====> 0.212657
>