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In this R Tutorial, we will complete Powerball data analysis based on the odds of winning the Powerball. Playing the Powerball is only a mere $2 a ticket, which is half the cost for a cup of coffee. Now if that $2 ticket hit the Jackpot then the reward would be most benefiting.
So what are the odds of winning?
- Grand Prize -> Match 5 white balls and the Powerball -> 1 in 292,201,338.00
- $1,000,000 -> Match 5 white balls -> 1 in 11,688,053.52
- $50,000 -> Match 4 white balls and the Powerball -> 1 in 913,129.18
- $100 -> Match 4 white balls -> 1 in 36,525.17
- $100 -> Match 3 white balls and the Powerball -> 1 in 14,494.11
- $7 -> Match 3 white balls -> 1 in 579.76
- $7 -> Match 2 white balls and the Powerball -> 1 in 701.33
- $4 -> Match 1 white ball and the Powerball -> 1 in 91.98
- $4 -> Match the Powerball -> 1 in 38.32
So the odds of winning the Grand Prize are 1:292,201,338 but it would cost double to buy all variations of the tickets since each ticket is $2.
What is the Powerball?
The Powerball is made of 69 white balls and only 5 will be drawn. In addition, there are 26 red balls (Powerball) which will total 6 balls that need to match the drawing in order to win the Grand Prize. The Powerball drawings are every Wednesday and Saturday night at 10:59 p.m. EST (Eastern Standard Time AMERICAS). we draw five white balls out of a drum with 69 balls and one red ball out of a drum with 26 red balls.
Creating Powerball Match and Prize Variables
Below are the variables that are created from top prize to no prize and the corresponding output for each.
Match 5 white balls and the Powerball
Input:
white_5_red_1 <- c(5,1)
One Winner for the total Grand Prize
Input:
grand_prize <- "You won the Grand Prize of $900,000,000"
Match 5 white balls and 0 Powerball
Input:
white_5_red_0 <- c(5,0)
Second Powerball prize of $1,000,000
Input:
second_prize <- "You won the Grand Prize of $1,000,000"
Match 4 white balls and the Powerball
Input:
white_4_red_1 <- c(4,1)
Third Powerball prize of $50,000
Input:
third_prize <- "You won the Grand Prize of $50,000"
Match 4 white balls and 0 Powerball
Input:
white_4_red_0 <- c(4,0)
Fourth Powerball prize of $100
Input:
fourth_prize <- "You won the Grand Prize of $100"
Match 3 white balls and the Powerball
Input:
white_3_red_1 <- c(3,1)
Fifth Powerball prize of $100
Input:
fifth_prize <- "You won the Grand Prize of $100"
Match 3 white balls and 0 Powerball
Input:
white_3_red_0 <- c(3,0)
Sixth Powerball prize of $100
Input:
sixth_prize <- "You won the Grand Prize of $7"
Match 2 white balls and the Powerball
Input:
white_2_red_0 <- c(2,0)
Seventh Powerball prize of $7
Input:
seventh_prize <- "You won the Grand Prize of $17"
Match 1 white ball and the Powerball
Input:
white_1_red_1 <- c(1,1)
Eighth Powerball prize of $4
Input:
eighth_prize <- "You won the Grand Prize of $4"
Match 0 white balls and the Powerball
Input:
white_0_red_1 <- c(0,1)
Ninth Powerball prize of $4
Input:
ninth_prize <- "You won the Grand Prize of $4"
Match 0 white balls and the Powerball
Input:
white_0_red_0 <- c(0,0)
No Powerball prize
Input:
no_prize <- "No luck this time, try again"
R else if() statements
In order to create a function statement to verify which prize a person may win, a functional else if() statement will work. The function works because it will allow several conditions to be checked. We will be able to use the above variables and creation a function that will print which prize you won or didn’t win.
Output:
powerball_numbers <- function(x) {if(identical(x,white_5_red_1)){grand_prize}
else if(identical(x,white_5_red_0)){second_prize}
else if(identical(x,white_4_red_1)){third_prize}
else if(identical(x,white_4_red_0)){fourth_prize}
else if(identical(x,white_3_red_1)){fifth_prize}
else if(identical(x,white_3_red_0)){sixth_prize}
else if(identical(x,white_2_red_0)){seventh_prize}
else if(identical(x,white_1_red_1)){eighth_prize}
else if(identical(x,white_0_red_1)){ninth_prize}
else if(identical(x,white_0_red_0)){no_prize}
}Now with the above function, we can manually input the white ball and red ball variable to match the number of white balls and the Powerball.
Input:
powerball_numbers(c(5,1))
Output:
[1] "You won the Grand Prize of $900,000,000"
Let’s try two more but pick 0-5 for the white balls and either 0 or 1 for the Powerball.
Input:
powerball_numbers(c(3,0))
Output:
[1] "You won the Grand Prize of $7"
Input:
powerball_numbers(c(0,0))
Output:
[1] "No luck this time, try again"
Calculate the Powerball Odds
If we’re looking to win the Powerball second prize, we would need to match the 5 white numbers that will be drawn. There are exactly 5 * 4 * 3 * 2 * 1 different orders that are known as 5 factorial.
Mathematical choose() Function
The choose() function returns binomial coefficients and the logarithms of their absolute values. The choose() function will be used because it is defined for all real numbers n and integer k (choose(n, k)).
While utilizing this function, we can start to build variables based on the Grand Prize and the count of white balls and red balls (Powerball).
So how we do we calculate?
Since the order would be 5 * 4 * 3 * 2 * 1 with a total of 69 white balls then the probability of matching all of the main numbers in Powerball would look like below.
Input:
> choose(69,5)*26
Output:
[1] 292201338
This shows us that the odds to match all 5 white balls plus the Power ball will be 1 in 292,201,338.