Odds Calculations

[PJM1206]

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?

[pzhon]

[ 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 (http://www.google.com/search?sourceid=navclient&ie=UTF-8&rls=GGLD,GGLD:2004-24,GGLD:en&q=%284+choose+2%29+%2A+%2876+choose+18% 29+%2F+%2880+choose+20%29).

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%