How to Play Powerball
Powerball is played by selecting six numbers. Five numbers from 1 through 69 (white balls) and one number from 1 through 26 (red balls). Each number is on a special ball that is randomly selected by a machine during the drawing. To win the jackpot, your goal is to match every number selected by the machine. Your first five numbers (white balls) do not have to be in the same order as the balls that are selected from the machine. However, your one number for the red ball must match exactly.
It costs $2 for a single play. Profits from every ticket bought goes towards funding K-12 education.
Changes in Powerball
The number of balls and the odds of winning change regularly. In 2015, Powerball made changes in the game. The change in the odds was a result of increasing the number of white balls that can be drawn from 59 to 69 numbers and decreasing the number of red balls from 35 to 26. That decreased the odds of winning the jackpot from 1 in 175 million to 1 in 292 million.
How?
For the first event (white balls), you choose 5 out of 69 numbers. Then for the second event (red balls), you choose 1 out of 26 numbers. The order of the numbers does not matter, therefore there are (69C5)(26C1) = (11,238,513)(26) = 292,201,338 distinct groups of numbers that may be selected from the machine. Therefore, the probability of the machine drawing a player's distinct group of numbers and winning the jackpot is 1 / 292,201,338 = .0000000034.
In March of 2020, due to the lack of players during the pandemic, the Powerball jackpot changed from a minimum of $10 million to a $2 million standard increase between drawings if there is no winner. This helps build huge jackpots if no one wins for several weeks. Powerball's minimum starting jackpot also dipped from $40 million to $20 million.
Assignment
What if we invented a game called GrandoSphere. GrandoSphere is played by selecting six numbers. Five numbers from 1 through 20 (white balls) and one number from 1 through 5 (red balls). Each number is on a special ball that is randomly selected by a machine during the drawing. To win the jackpot, your goal is to match every number selected by the machine.