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Mark Six

(Question raised by Dr. T.W. NG.) The following is some ten draws of the Mark Six Lottery in reverse order.

(i) One can always find at lease 2 drawn numbers having the same first digit.

(ii) Very often (9 out of 10 in the Table below) one can find at least 2 drawn numbers having the same last digit. Is it reasonable to have this high chance ?

For simplicity of calculation, you may assume the total number of balls is 50 instead of 49.

You can get another set of MarkSix results via here.

Draw Number Draw Results Same digit found
1 + YES
2 + YES
3 + NO
4 + YES
5 + YES
6 + YES
7 + YES
8 + YES
9 + YES
10 + YES
Department of Mathematics, HKU, 2010