Calculate Lotto Probability of 20 Numbers in 6 of 45 Lotto Game

An Australian lottery player wants the formula to calculate the probability or odds for a 20-number system in a lotto game that draws 6 winning numbers from a field of 45.

Posted by Dazza on August 02, 2000.

In a 6 from 45 lotto, how do you work out the probability of getting all 6 numbers if you purchase a system 20 (pick 20 lotto numbers) entry?

Follow Ups:

• Probabilities for 20 lotto number system in a 6 of 45 lotto game Ion Saliu 8/02/2000.

Resources in Theory of Probability, Mathematics, Software

• Theory of Probability: Best introduction, formulae, algorithms, software.

• Fundamental Formula of Gambling.
• Mathematics of Fundamental Formula Of Gambling.
• Combinatorial Mathematics: Calculate, generate exponents, permutations, sets, arrangements, combinations for any numbers and words.

• Standard Deviation: Theory, Algorithm, Software.
  Standard deviation: Basics, mathematics, statistics, formula, software, algorithm.
• Standard Deviation, Gauss, Normal, Binomial, Distribution
  Calculate: Median, degree of certainty, standard deviation, binomial, hypergeometric, average, sums, probabilities, odds.

• Caveats in Theory of Probability.
• Birthday Paradox: Mathematics, Probability, Software.

• Download Probability, Mathematics, Statistics, Combinatorics Software.

Comments:
: Lotto Probability Question. In a 6 from 45 lotto, how do you work out the probability of getting all 6 lotto numbers if you purchase a system 20 (pick 20 numbers) entry? Total combinations for the 6/45 game: : C(45 taken 6 at a time) = 8,145,060 lotto combinations. : Total combinations of 20 lotto numbers taken 6 at a time: C(20, 6) = 38,760. : The probability to get the 6 lottery winners in the 20-number bloc: : 38,760 / 8,145,060 = 0.48% (less than half a percentage point). : You can expect 6 winners once in 200 drawings. : As I showed several times, it's best to use WHEEL-6 lotto software with filters. You can also use the WHEEL45.36 system you can find on the download site. You still need to use it in conjunction with PURGE-6. If you are totally new to this site and my software, you could feel out of luck in the first moment. But after some searching, many pieces will fall in place. Title: "Calculate lotto probability of 20 numbers in a 6 of 45 lotto game". Lottery player in Australia wants the formula to calculate the probability or odds for a 20-number system in a lotto game that draws 6 winning numbers from a field of 45.