How to Calculate Lottery Probability

Updated April 17, 2017

Lotteries are very common and also very popular. The specific odds of winning a given lottery depend on a variety of factors, including the manner in which the lottery is organised and the number of tickets purchased. If these details are known, some basic probability calculations can determine your odds of winning. The well known Canadian 6/49 lottery provides a good example of how lottery odds can be determined.

Determine how many numbers the lottery has to pick from (call this "n") and what quantity of numbers it actually picks (call this "r"). In the Lotto 6/49 lottery, six numbers are chosen from the set consisting of 1 through 49, so n would be 49 and r would be 6.

Determine how many possible outcomes the lottery process has. This is the total number of possible results from the lottery process and can be found using the equation n!/(r!)(n-r)! where n! means n x (n-1) x (n - 2) x ... x 1. In the case of Lotto 6/49, the number of unique six-digit combinations that can be chosen from between 1 and 49 is 49!/(6!)(49-6)!, which equals 13,983,816. This number will be referred to as "M."

Determine how many of these unique combinations you have available as potential winning numbers. Purchasing one ticket typically gives one possible winning number, two tickets gives two possible winning numbers and so on. This number will be "m."

Calculate the ratio of m/M. This is the probability of winning the lottery based on the number of tickets purchased. The odds of winning Lotto 6/49 with 1 ticket, therefore, are 1/13,983,816.

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About the Author

Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.