I have done a lot of thinking about the Powerball lottery recently – in a good way, not a lustful, fantasy, unhealthy way (well, maybe some of that, but not too much). Today, since I think most people find it interesting, I wanted to give a primer on calculating the odds of winning and then compare that to the odds of some other strange occurrences. Over the next few days, I will share my strategy for winning the lottery and finally share my thoughts on the moral and ethical implications of the lottery in our society.
Lottery Odds
Disclaimer: I know that I am a nerd. Please don’t feel the need to inform me of that fact in a response.
Calculating your odds for winning the lottery is very easy. You basically figure out how many ways you can win and divide it by the total number of ways the balls could be picked.
In the Powerball Lottery, they have 55 balls in the hopper. They pick 5 balls out of the hopper. Then they put all the balls back in before picking the final ball - the Powerball.
Let’s say that the winning numbers are: 5 - 21 - 33 - 44 - 55 and that the Powerball is 12.
So, our chance of getting the 1st ball correct is 1 / 55.
Our chances of getting the 2nd ball correct is 1 / 54 (only 54 balls left to choose from).
Our chance of getting the 3rd ball correct is 1 / 53 (only 53 balls left to choose from)
And so on.
To get all 5 numbers you correct, you must correctly select the first number AND the second number AND the third number, etc. Not only that, but they put all the numbers back in the pot before selecting the powerball number.
So, my chances of selecting the powerball correctly are back to 1/55.
In the world of mathematics when “this AND that” have to be true, that means MULTIPLY your chances together. Think in terms of a coin flip or having babies. The chances of getting tails (or having a boy) are approximately 1 in 2. If you have two coin flips (or have two kids), the chances of tails coming up both times (or having two boys) is 1/2 x 1/2 or ¼ . The chances of tails coming up three times in three coin flips (or having three children – all boys) is ½ X ½ X ½ = 1/8.
So, the chance of picking the right lottery number is:
1/55 X 1/54 X 1/53 X 1/52 X 1/51 X 1/55 (remember they put all the numbers back in when picking the powerball – that is why we multiply by 1/55 at the end)
This calculates out to: 1 in 2.3 trillion.
But, wait, there is good news. The calculation above assumes that you pick the numbers in the exact order in which they were drawn. The reality is that if the winning numbers were: 5 - 21 - 33 - 44 - 55 Powerball: 12
Then we would be winners if any of the following scenarios played out:
21 - 44 - 55 - 5 - 33 Powerball: 12
OR
55 - 5 - 21 - 33 - 44 Powerball: 12
OR
5 - 33 - 44 - 55 - 21 Powerball: 12
Etc.
The reality is that there are 120 different ways to arrange these numbers. Using the same logic we used above, this can be calculated by multiplying the numbers together:
5 X 4 X 3 X 2 X 1 = 120
Notice that we are picking a total of 6 numbers – not 5, but since the powerball is fixed (in other words it always has to be the last ball picked), it does not factor into this calculation.
If we were picking 7 numbers (including the powerball), the calculation would be:
6 X 5 X 4 X 3 X 2 X 1 = 720
But, we are not picking 7 numbers we are picking 6 (5 normal numbers and 1 powerball number). So, we really have 120 chances in 2.3 trillion to pick the right numbers.
This simplifies to: 1 in 191,331,855.
To put this number in perspective:
-there are approximately 300 million people living in the United States
-the chance of drowning in a bathtub is 1 in 818,534
-the chance of dying due to being struck by lightning is 1 in 4.4 million
-the chance of dying due to exposure to hot tap water is 1 in 7.2 million.
-the chance of dying by legal execution (e.g. electric chair, lethal injection, etc.) is 1 in 4.3 million (of course, this number is higher if you live in Texas).
-the chance of a woman giving birth to quadruplets is 1 in 705,000
Seems, hopeless doesn’t it. In reality it is; however I have a plan. I will share that tomorrow.
Upcoming Posts:
1. Strategy for winning the lottery and my opinion on lotteries in general.
2. My review of the movie: The Lakehouse
3. My thoughts on paradigm shifts
