Lottery Research

The numbers picked for the prizes consist of 5 white balls picked at random from a drum that holds 55 balls numbered from 1 to 55. The Power ball number is a single ball that is picked from a second drum that has 42 numbers ranging from 1 to 42. If the results of these random number selections match one of the winning combinations on your lottery ticket, then you win something. In any combinatoric problem where all possible outcomes are equally likely, the probability of a successful outcome is determined by finding the number of successful combinations, and then dividing by the total number of all combinations. There are nine possible configurations that will win something in the Power ball Lottery. For each of these, the probability of winning equals the number of winning combinations for that particular configuration divided by the total number of ways the Power ball numbers can be picked.

The power ball combinations are, since the total number of combinations for Power ball numbers is used in all the calculations, we will calculate it first. The number of ways 5 numbers can be randomly selected from a field of 55 is: COMBINATION (55, 5) = 3,478,761. For each of these 3,478,761 combinations there are COMBINATION (42, 1) = 42 different ways to pick the Power ball number. The total number of ways to pick the 6 numbers is the product of these. and the total number of equally likely Power ball combinations is 3,478,761 x 42 = 146,107,962.

The number of ways the 5 numbers on your lottery ticket can match the 5 white balls is COMBINATION (5, 5) = 1. The number of ways your Power ball number can match any of the 41 losing Power ball numbers is: COMBINATION (41, 1) = 41. (Pick any of the 41 losers.) Thus there are COMBINATION (5, 5) x COMBINATION (41, 1) = 41 possible combinations. The probability for winning $200,000 is thus 41/146,107,962 = 0.000000280614 or “One chance in 3,563,608.83”.

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