Lottery odds

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patthefish

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My sports club run a lottery, pick 4 numbers from a possible 32 numbers 1 to 32. The numbers are picked each Thursday. We sell about 300 tickets each week. How often should it be won?
 
There are \(\displaystyle \frac{32!}{4!(28!)}=35960\) ways to choose 4 numbers out of 32.

The probability of winning with one ticket is \(\displaystyle \frac{1}{35960}\)

So, the probability that of the 300 tickets there is a winner would be

\(\displaystyle \frac{300}{35960}=\frac{15}{1798}\approx .00834\) or about .834%
 
Thanks for your reply Galactus.
We sell about 300 tickets each week and draw numbers once a week.
How often in weeks should we expect it to be won outright?



galactus said:
There are \(\displaystyle \frac{32!}{4!(28!)}=35960\) ways to choose 4 numbers out of 32.

The probability of winning with one ticket is \(\displaystyle \frac{1}{35960}\)

So, the probability that of the 300 tickets there is a winner would be

\(\displaystyle \frac{300}{35960}=\frac{15}{1798}\approx .00834\) or about .834%
Click to expand...
 
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