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August 24th, 2017, 10:36 AM  #1 
Newbie Joined: Aug 2017 From: Texas Posts: 1 Thanks: 0  Beginner/Basic  Probability  Guessing Incorrectly
All, First, I am not a statistics guy or really a math guy. My question is a result of the recent PowerBall  "What are the odds of not drawing any correct balls?" I know that the odds of winning are: (5/69)*(4/68 )*(3/67)*(2/66)*(1/65)*(1/26) I worked the logic for that by playing with a 2 digit number out of 0099: (2/10)*(1/10)= 20% That makes sense the possible correct numbers are 12 or 21, etc On my 2 digit example, the odds of getting no numbers correct is 80% (just by logic  I hope). However, the "math" I came up with is wrong: (8/10)*(9/10) = 72% I guess somehow the denominator of the 2nd term should be 9, yielding: (8/10)*(9/9) and the 80% that makes sense. But I can;t understand why that denominator would be 9. I think if I understood what I was doing wrong on the simple example, I could then develop the answer to  what are the odds of drawing no correct balls in the PowerBall Thanks in advance. 
August 24th, 2017, 10:58 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,975 Thanks: 1026 
on the first white ball you have 64 possible balls that don't match any of the winning balls. and similarly for the rest of the white ball draws. there are 25 possible nonmatching red balls. so $p = \dfrac{64}{69}\dfrac{63}{68}\dfrac{62}{67}\dfrac{6 1}{66}\dfrac{60}{65}\dfrac{25}{26} = \dfrac{31768800}{48700223} \approx 0.65$ 

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beginner or basic, guessing, incorrectly, probability 
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