Lottery odds calculator
The general case: pick any pool and any number of balls, with or without a bonus ball.
Odds of that match: one in
13 983 816.00
- Odds of the jackpot: one in
- 13 983 816
- Ways to achieve that match
- 1
- Total possible outcomes
- 13 983 816
- Chance of that match
- 0.000 007 151 12 %
- Chance of matching at least one number
- 0.564 035
Show the working
- Numbers in the pool = 49
- Numbers drawn = 6
- Numbers you want to match = 6
- Bonus pool = 1
- Bonus numbers drawn = 0
- total_main = comb(49, 6) = 13 983 800
- total_bonus = 0 > 0 ? comb(1, 0) : 1 = 1
- Total possible outcomes = 13 983 800 * 1 = 13 983 800
- Ways to achieve that match = comb(6, 6) * comb(49 - 6, 6 - 6) = 1
- probability = 13 983 800 > 0 ? 1 / 13 983 800 : 0 = 7.15112e-8
- Odds of that match: one in = 7.15112e-8 > 0 ? 1/7.15112e-8 : 0 = 13 983 800
- Odds of the jackpot: one in = 13 983 800 > 0 ? 13 983 800 : 0 = 13 983 800
- Chance of that match = 7.15112e-8 * 100 = 0.000 007 151 12
- Chance of matching at least one number = 13 983 800 > 0 ? 1 - comb(49 - 6, 6)/13 983 800 : 0 = 0.564 035
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- ways to match k of n drawn from a pool of N = C(n,k) x C(N-n, n-k)
- probability = ways / C(N, n)