How Much Does Powerball Pay For Matching 3 Numbers
If you spend a few dollars playing the multi state Powerball lottery every week, but have never won a prize, you might be wondering just what your chances are to actually hit the jackpot. With a few mathematical equations, you can figure out what your chances are of quitting your job any time soon.
To figure out your odds of winning the Powerball jackpot, first you will need to know the number of balls in play. The white balls, which are selected from one drum and make up the first five numbers on your ticket, range in number from 1 to 55. The Powerball, which is selected from a different drum, can range from 1 to 42. These numbers will help you find the total possible number of Powerball number combinations, which you will need to have to calculate your odds of winning. The easiest way to calculate the number of winning combinations is to use your Excel program and the COMBIN feature. If you plug in what you know about the first five balls - that they range in number from 1 to 55 and that five you will be selected - you will discover that there are 3,478,762 possible combination outcomes. Now, to factor the sixth ball, the Powerball, into the equation, you need to multiply the possible outcomes by the possible number of Powerballs; which is 42. Thus you will find out that there are 146,107,962 possible winning combinations in a Powerball drawing.
There are nine different ways to win something at Powerball, and each way has its own probability. Calculating your odds of winning the whole jackpot by matching all five numbers, plus the Powerball, is easy when you know the number of possible winning combinations; your chance of matching everything exactly is 1 in 146,107,962. Figuring out the other equations gets a little more complex, but a general rule of thumb is to divide the number of possible winning combinations by the number of total possible combinations.
For instance, consider your odds of matching four out of the five balls, and matching the Powerball. There are five ways that four of your choices out of five can match four of the five numbers for of the white balls, and 50 a number on your ticket can match the any of the losing numbers (because there are 55 numbers to choose from in total). The number of ways you can match the Powerball is one. If you multiply those chances together, you get 250 chances. Then, divide those 250 chances by the total number of chances, and you get your odds. So, your odds of matching four numbers plus the Powerball are one in 584,431.85.
Now consider your odds of matching four out of the five numbers, and not matching the Powerball. The same figures hold true as they did in the equation above; there are five ways to match four numbers, and 50 ways to match one of the losing numbers from the white balls. But this time, you want to use the number of ways to match a LOSING Powerball number; which is 41. Multiply those chances together, and you discover your odds of matching four out of five numbers and not matching the Powerball is 10,250. Divide that by the total number of chances. Your odds of winning under this scenario are one in 14,255.44.
These formulas will allow you to calculate your odds of winning in all nine possible ways. If you add all your chances of winning together, you will get your total odds of winning any prize at all; which is one in 36.61. So, though your odds of winning the big cash are slim, your odds of some kind of pay out are good enough to justify that weekly ticket!