Megamillions number frequency - probability puzzlePrev TopicNext Topic

• Orange71

  

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  Nov 17, 2023, 1:46 pm

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  In Megamillions there are 70 numbers in the main lotto pool (not counting the Megaball). 5 numbers are drawn from this pool in each game. Consider 50 random game draws. What is the probability that at least one number (ball) will (a) never occur in the 50 draws, and (b) occur in at least 10 game draws?
• Orange71

  

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  Nov 22, 2023, 8:03 pm

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  Here are the probabilities for question (a), at least one ball does not occur in multiple game draws. "N" is the number of game draws. For 50 draws the probability is 84.01%. As you can see, the probability distribution has a long tail, and is thus very right-skewed.

  N	Prob
  30	0.999929
  35	0.997918
  40	0.982929
  45	0.934073
  50	0.840123
  55	0.711815
  60	0.571840
  65	0.440267
  70	0.328311
  75	0.239218
  80	0.171456
  85	0.121477
  90	0.085378
  95	0.059673
  100	0.041547
  105	0.028850
  110	0.019997
  115	0.013843
  120	0.009575
  125	0.006619
  130	0.004573
  135	0.003159
  140	0.002182
  145	0.001507
  150	0.001040
  155	0.000718
• Wavepack

  

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  The mathematics and reasoning used to arrive at the answer is more interesting to me than just the answer.

  What IDE do you use for Python?  Though I mostly analyze in Matlab, I dabble in Python to help verify analysis of the NZ whistleblower data in regards to excess deaths and Covid shots.   For Python, the IDE I currently use is VSCode with the Python, PyLance, and Git extensions.
• Orange71

  

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  Dec 11, 2023, 8:20 pm

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  In response to Wavepack

  Quote: Originally posted by Wavepack on Dec 6, 2023

  The mathematics and reasoning used to arrive at the answer is more interesting to me than just the answer.

  What IDE do you use for Python?  Though I mostly analyze in Matlab, I dabble in Python to help verify analysis of the NZ whistleblower data in regards to excess deaths and Covid shots.   For Python, the IDE I currently use is VSCode with the Python, PyLance, and Git extensions.

  I usually use VScode, but I have Anaconda installed, so all the pursuant data science packages with Anaconda (e.g. Numpy, Scipy, Pandas, etc.) are available by import. I also have a few packages that are not available with conda install, so I use PIP instead. 

  For this particular problem I did not code a  Python app, rather I just used an Excel spreadsheet. Certainly you could write a Python app if you want.

  Here's the algorithm for calculating the probability for problem (a). I put problem (b) out there, but I'm finding it's much harder to solve.

  N = number of game draws (e.g. 30, 40, 50, etc.)

  
• Wavepack

  

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  Dec 12, 2023, 4:33 pm

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  Seeing the form of the answer, I'm now interested in knowing why it's true.   A proof would be nice to learn from.

  What math formatter did you use to express the formula?
• wander73

  

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  Dec 12, 2023, 4:49 pm

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  Frequency,  you mean pattern.  According to someone I know of ,  this person knows someone else that has won over $5 million and knows which numbers in the pattern that will hit.
• mathematic6G

  

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  Dec 12, 2023, 8:05 pm

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  I'm new here and I would like to share my studies with the dreamers.

  I know the Power ball# is not 9, 13, 21, 23, 25, 4, 16, 18.

  You can thank me later.
• Wavepack

  

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  ^ The Powerball was 18 on Dec 13, 2023.
• Brock Lee

  

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  In response to mathematic6G

  Quote: Originally posted by mathematic6G on Dec 12, 2023

  I'm new here and I would like to share my studies with the dreamers.

  I know the Power ball# is not 9, 13, 21, 23, 25, 4, 16, 18.

  You can thank me later.

  is it now late enough to thank you?