Powerball: How many sets of numbers should I get?

Powerball Lottery Ticket

Powerball Lottery Ticket

Today, 17 Aug 2017, the California powerball pot is at $700M. Wouldn’t it be nice to win that and tell your boss the next day that you won’t be coming in to work because you won the lottery?

Everyone dreams of that but sometimes take no action. Remember, you have to take action to at least have a chance of winning. That said, the question begs to be asked: How many sets of numbers would be best to get to improve one’s chance of winning?

The answer is simply one set. This will cost you just $2.00. Here’s why…

 

What’s the chance of getting the correct number?

Let’s first understand the powerball numbering setup.

  1.  You are to pick 5 numbers from 1 to 69.
  2. Then pick a number from 1 to 26

To figure out your chances of picking the right number you use probability theory, which says:

  • The chances of you picking the right number from 1 to 69 is 1 out of 69, or 1/69 multiplied to…
  • The chances of you picking the right second number out of 68 numbers that are left, which is 1/68 multiplied to …
  • The chances of you picking the right third number out of 67 numbers that are left, which is 1/67 multiplied to…
  • The chances of you picking the right fourth number out of 66 numbers that are left, which is 1/66 multiplied to…
  • The chances of you picking the right fifth number out of 65 numbers that are left, which is 1/65 multiplied to …
  • The chances of picking the right number out of 26, which is 1/26.

This equates to 1/69 X 1/68 X 1/67 X 1/66 X 1/65 X 1/26 or 1/(69X68X67X66X65X26) or 1/35,064,160,560 or 2.852xe-11 or 0.00000000002852.

Essentially, your chances of picking the right number is roughly 1 in 35 billion.

Let’s say you decided to buy 10 sets of numbers.  This changes your chances from 1 in 35 billion to 10 in 35 billion.  Does that really make any mathematical difference?  The answer is NO.  You chances went from 0.00000000002852. to 0.0000000002852.  Let’s say you decided to buy 1000 sets (cost is $2000).  This changes your chances to 0.000000002852.  Say that you are rich and had $2M to spare.  You buy 1M sets of numbers.  This improves your chances of winning to 0.000002852.  Still practically 0!

Besides if you’re that rich, why even buy a lottery ticket?

The bottom line:  buy one set of numbers for $2.

That’s it.


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