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Mathematical story of vaccine
(a) the batch number of vaccines selected in the three districts is 43=64, (2 points).

There are just two areas with the same vaccine batch number, and the number of species is C32A42=36, (3 points).

The probability of selecting the same vaccine batch number in exactly two of the three districts is p = 916; (6 points)

(two) the number of areas with the same vaccine batch number. Possible values are 0, 2, 3, (8 points).

p(ζ= 0)= a 3443 = 38,p(ζ= 2)= 9 16,p(ζ= 3)= c 1443 = 1 16,(65438。

The distribution list is:

eξ= 0×38+2×9 16+3× 1 16 = 2 1 16。 (12)