Ultra Lotto 6/58 First Digit Probability

Grouped into six by their first digit, the following is how I grouped the 58 lotto numbers.

• Group 1 (G1) comprises the lotto numbers 01-09
  
• Group 2 (G2), lotto numbers 10-19
• Group 3 (G3), lotto numbers 20-29
• Group 4 (G4), lotto numbers 30-39
• Group 5 (G5), lotto numbers 40-49
• Group 6 (G6), lotto numbers 50-58

Is it possible that the winning numbers would mostly come from a particular group? Let's find out.

Statistics says, based on 325 results ~

Win Result	G1	G2	G3	G4	G5	G6
0	30.8%	26.8%	31.4%	32.6%	32.6%	33.2%
1	44.0%	44.0%	42.8%	42.2%	42.2%	43.7%
2	20.0%	25.2%	22.2%	17.8%	18.8%	18.8%
3	4.9%	3.4%	3.7%	6.5%	6.2%	4.0%
4	0.3%	0.6%	0.0%	0.9%	0.3%	0.3%
5	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
6	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%

Observations

• No 6 winning numbers came from one group alone. Therefore, 10•12•13•14•15•16 or 20•22•23•24•25•26 or something similar is very unlikely to happen. The probability is 0%.
• Likewise, no 5 winning numbers came from one group alone.
• Though there were a few cases when 4 winning numbers came from one group alone, the probability is very low, ranging from 0% to 0.9%. If such occurred, it was an extraordinary case. For example, the result of 5 Aug 2016 02 • 06 • 08 • 09 • 30 • 52 is a very extraordinary case, 4 numbers coming from the single unit group.
• Three winning numbers coming from one group alone is also rare. The probability ranges from 3.4% to 6.5%. These are exceptional cases. The result of 3 Dec 2017 14 • 15 • 23 • 40 • 43 • 47 is an example of a rare case wherein 3 numbers came from the group of 40s.
• The probability of 2 winning numbers coming from one group alone ranges from 17.8% to 25.2%. Collectively, however, this case has occurred 265 times out of 325 results, a probability of 81.5%. It means that it is safe to play 2 numbers coming from one group.
• The strongest probability is that 1 number from each group can almost definitely win. This case has occurred 313 times out of 325 results, a strong probability of 96.3% with plus or minus 2.7% margin of error at 99% confidence level. This means that this statement is 93.6% to 99% closer to truth.
• However, it is also possible that a particular group would not produce a winning number. Almost all results, 319 all in all out of 325, recorded such case. In fact, it is more probable that a group would produce no winning number than to produce 2 winning numbers. It is but logical that if a group produced 2 winning numbers, one group would produce none. This statement has a probability of 98.15% with a 1.93% margin of error.

Conclusion

Based on the preceding observations, a winning combination commonly consists of 2 numbers coming from one group, while the rest give 1 winning number each. An example would be 03 • 15 • 22 • 31 • 34 • 52 from 8 Sep 2017 draw result wherein the group 30s produced 2 winning numbers while the group 40s produced none. All the rest gave 1 winning number.