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a state lottery offers a came with the following setup

Choose five (5) numbers from (0 through 9) or use the Quik Pik option and let the computer select for you.

You win by matching your numbers to the winning number(s) drawn in the EXACT ORDER AND POSITION in a single PLAY.

Match all FIVE of your numbers in EXACT ORDER to the winning numbers to win the top prize of $10,000!

******** what are the odds of : - purchasing 30 QuickPick tickets - Each of the 30 seperately generated and printed tickets: have the same digit 0-9 in all 5 of the positions Example: 11111, 99999, 00000, 44444,
With multiple duplicate tickets generated Example: 6 (six) copies of 00000 4 (four) copies of 77777

the lotter office claims: - Quik Pick generates each digit randomly to comprise each ticket Odds of any number combo is 1. in 100,000

What are the odds of 30 consequtive "random" numbers also being duplicated identical digit 0-9 in all 5 positions.

Is it reasonable to consider this situation a "random generation of 5 random digits 0-9 as truly random???

M Long
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  • To start your work: the probability of any particular ticket in one QuickPick or one lottery draw is $1/100000$. There is nothing special about $11111$ even though it looks special to you. – Ethan Bolker Mar 19 '24 at 21:56
  • The probability of getting 5 of the same digit on a Quik Pick should be $\frac{10}{100000}$ or 1 in 10,000. The probability of this happening 30 times in a row is 1 in $10^{120}$. In comparison, there are about $10^{80}$ elementary particles in the universe. – Karl Mar 19 '24 at 21:59
  • Related: https://math.stackexchange.com/questions/4080732 – Karl Mar 19 '24 at 22:04

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