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Odds Calculations
I was trying to calculate the odds of winning a KENO bet. I picked 4 numbers 2,10,13,23. There are 80 possible numbers that can come up 1 through 80. The ticket cost $1.00 and pays $1 if two numbers hit, $4 if 3 numbers hit and $100 if all 4 numbers hit. I calculated the odds of 2 numbers coming up as 499 to 1: 4/80*3/79*76/78*75/77=.002 or 499:1 and the odds for all 4 numbers 4/80*/3/79*2/78*1/77= .000006 or 158M :1??? Is that correct?
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Re: Odds Calculations
[ QUOTE ]
I calculated the odds of 2 numbers coming up as 499 to 1: 4/80*3/79*76/78*75/77=.002 or 499:1 and the odds for all 4 numbers 4/80*/3/79*2/78*1/77= .000006 or 158M :1??? Is that correct? [/ QUOTE ] No. If only 4 numbers were chosen, it would be correct if the numbers had to be in that order: Hit, Hit, Miss, Miss. Neither assumption is correct. In keno, 20 numbers are drawn out of 80. The number of ways you can get two hits is 4C2 * 76C18, so the probability of getting two hits is ((4 choose 2) * (76 choose 18)) / (80 choose 20) = 0.212635466. Here are the probabilities of getting each number of hits: 0: 30.83% 1: 43.27% 2: 21.26% 3: 4.32% 4: 0.31% |
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