Lana had placed 4 red and 6 blue marbles in her bag.
Lois had placed 3 red and 5 blue marbles in her bag.
DEFDBL A-Z
FOR red = 1 TO 15
FOR col = 4 TO 6
p = col / (col + red) * (col - 1) / (col + red - 1)
* (col - 2) / (col + red - 2) * (col - 3) / (col + red - 3)
PRINT red; col,
PRINT USING "#.#######"; p
NEXT
NEXT
produces the following table (which, though, has since been sorted on the probability column):
15 4 0.0002580
14 4 0.0003268
13 4 0.0004202
12 4 0.0005495
11 4 0.0007326
10 4 0.0009990
15 5 0.0010320
14 5 0.0012900
9 4 0.0013986
13 5 0.0016340
8 4 0.0020202
12 5 0.0021008
15 6 0.0025063
11 5 0.0027473
7 4 0.0030303
14 6 0.0030960
10 5 0.0036630
13 6 0.0038700
6 4 0.0047619
12 6 0.0049020
9 5 0.0049950
11 6 0.0063025
8 5 0.0069930
5 4 0.0079365
10 6 0.0082418
7 5 0.0101010
9 6 0.0109890
4 4 0.0142857
8 6 0.0149850
6 5 0.0151515
7 6 0.0209790
5 5 0.0238095
3 4 0.0285714
6 6 0.0303030
4 5 0.0396825
5 6 0.0454545
2 4 0.0666667
3 5 0.0714286
4 6 0.0714286
3 6 0.1190476
2 5 0.1428571
1 4 0.2000000
2 6 0.2142857
1 5 0.3333333
1 6 0.4285714
Only the rows for 3 red, 5 blue and 4 red 6 blue contain the same probability.
Based upon Enigma No. 1551, "The same chance", by Richard England, New Scientist, 27 June 2009.
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