Odds of Getting Other Possibilities in Choosing 6 From 49
One must divide the number of combinations producing the given result by the total number of possible combinations (for example, as explained in the section above). The numerator equates to the number of ways one can select the winning numbers multiplied by the number of ways one can select the losing numbers.
For a score of n (for example, if 3 of your numbers match the 6 balls drawn, then n = 3), there are ways of selecting n winning numbers from the 6 winning numbers. This means that there are 6 - n losing numbers, which are chosen from the 43 losing numbers in ways. The total number of combinations giving that result is, as stated above, the first number multiplied by the second. The expression is therefore .
This can be written in a general form for all lotteries as:, where is the number of balls in lottery, is the number of balls in a single ticket, and is the number of matching balls for a winning ticket.
The generalisation of this formula is called the hypergeometric distribution (the HYPGEOMDIST function in most popular spreadsheets).
This gives the following results:
| Score | Calculation | Exact Probability | Approximate Decimal Probability | Approximate 1/Probability |
|---|---|---|---|---|
| 0 | 435,461/998,844 | 0.436 | 2.2938 | |
| 1 | 68,757/166,474 | 0.413 | 2.4212 | |
| 2 | 44,075/332,948 | 0.132 | 7.5541 | |
| 3 | 8,815/499,422 | 0.0177 | 56.66 | |
| 4 | 645/665,896 | 0.000969 | 1,032.4 | |
| 5 | 43/2,330,636 | 0.0000184 | 54,200.8 | |
| 6 | 1/13,983,816 | 0.0000000715 | 13,983,816 |
Read more about this topic: Lottery Mathematics
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