My Math Forum Beginner/Basic - Probability - Guessing Incorrectly

 Probability and Statistics Basic Probability and Statistics Math Forum

 August 24th, 2017, 11:36 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 00-99: (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, 11:58 AM #2 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,607 Thanks: 819 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 non-matching 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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