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1. Top Prize Level: Match all five numbers plus the Powerball (1 in 292,201,338 odds) Step 1: Calculate the number of ways in which 5 numbers can be chosen correctly out of 5 numbers drawn from 69 unique numbers. The formula is as follows: 5! ∗ (69−5)! =1∗ 64! = 64! =1 5!(5−5)! �(69−5)−(5−5)�!(5−5)! 0! (64−0)! 0! 64!1 This means that there is only 1 way in which 5 numbers out of 5 numbers drawn from a field of 69 numbers can be chosen correctly. Thus, there is only 1 chance in 11,238,513 of correctly choosing all five numbers drawn in the first portion of PowerBall. Step 2: Calculate how many ways the correct Powerball number can be chosen from 26 unique numbers. The chance of correctly choosing the Powerball is simply 1 in 26. Step 3: Determine the chance of choosing both correctly by multiplying these figures together: 1 ∗ 1 = 1 or 1 chance in 292,201,338. 11,238,513 26 292,201,338 2. Second Prize Level: Match all five numbers only (1 in 11,688,053.52 odds) Step 1: The chance of getting 5 numbers correct out of 5 numbers drawn from 69 unique numbers is 1 in 11,238,513 (see #1, Step 1 above.) Step 2: The chance of correctly choosing the Powerball is 1 in 26. Therefore, the chances of incorrectly choosing the Powerball are, conversely, 25 in 26. Step 3: Determine the chances of choosing 5 out of 5 of 69 correctly and getting the Powerball incorrect by multiplying these figures together: 1 ∗ 25 = 25 = 1 or 1 chance in 11,688,053.52. 11,238,513 26 292,201,338 11,688,053,52 (note: 0!=1)PDF Image | How to Calculate the Probabilities of Winning the Nine PowerBall Prize Levels
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