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
Famous quotes containing the words odds of, odds and/or choosing:
“The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle.”
—Hannah Arendt (1906–1975)
“However great a man’s fear of life, suicide remains the courageous act, the clear- headed act of a mathematician. The suicide has judged by the laws of chance—so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival.”
—Graham Greene (1904–1991)
“Let him be great, and love shall follow him. Nothing is more deeply punished than the neglect of the affinities by which alone society should be formed, and the insane levity of choosing associates by others’ eyes.”
—Ralph Waldo Emerson (1803–1882)