|Posted: March 1, 2007, 10:27 am - IP Logged|
Any set of numbers CA SLP can generate is capable of being duplicated in PB and MM. Therefore the limiting factor is CA SLP. The tone of your question does not specify that the numbers drawn in CA SLP have to be a specific set, so the odds of getting any specific combination in that game can be eliminated and the numbers drawn in both PB and MM must meet the smaller matrix requirements of CA SLP.
Formula for total PB possibilities, whether within the CA SLP matrix or not: ((55!/50!)/(5!))x42 = 146,107,962 possibilities.
Odds of any specific combination: 1::146,107,962.
Formula for total MM possibilities, whether within the CA SLP matrix or not: ((56!/50!)/(5!))x46 = 175,711,536 possibilities.
Odds of any specific combination: 1::175,711,536.
The odds of both PB and MM hitting any combination generated by CA SLP is simply a product of the odds of each game, or 1::25,672,854,424,849,632.
But I see the word "percentage" in your post, so that leads me to think that there may be more to the question than the above.
Formula for total CA SLP possibilities: ((47!/42!)/(5!))x27 = 41,416,353 possibilities.
Formula for the percentage of PB draws that will have all numbers drawn fall within the CA SLP 47/27 matrix: 41,416,353/146,107,962, or 28.346404%. Odds? 1::3.527784.
Formula for the percentage of MM draws that will have all numbers drawn fall within the CA SLP 47/27 matrix: 41,416,353/175,711,536, or 23.570651%. Odds? 1::4.242564.
The possibility of both PB and MM having all numbers drawn fall below 47/27 would be a product of the raw numbers above - 0.28346404 x 0.23570651, or 0.06681432. Percentage? 6.681432%. Odds? The reciprocal of the raw product, and/or the product of the above odds, or 1::14.966852.
Blessed Saint Leibowitz, keep 'em dreamin' down there.....
Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.