Home Mike's Geeky Stuff

SO YOU THINK YOU MAY WIN POWERBALL -

NOW EVEN LOWER CHANCES!

Just what are your chances? The numbers below have been changed since powerball went to 69 numbers in October 2015. Nobody remembers factorials or all the other probability stuff we learned but here is a crude but accurate way to figure out the odds.

  • To play, you choose 5 numbers between 1 and 69, and then one powerball between 1 and 26.

    Alright, you have made your picks and the powerball drawing starts. The first ball comes up - the chance of one of your numbers matching is 5 in 69 since you have 5 numbers sitting there. Congratulations, you have a match. Now, you have 4 numbers left.

    The second ball comes - there are 68 possible numbers so your chance of matching is 4 in 68. Wow, you match again. Now you have 3 numbers left.

    The third ball comes - you guessed it, your chance for a match is 3 in 67.
    fourth ball - 2 in 66.
    fifth ball - 1 in 65.

    Finally, the powerball - 1 in 26.

    So, the chance of having all that happen in one drawing is:

    5/69 * 4/68 * 3/67 * 2/66 * 1/65 * 1/26 = 120/35064160560 = 1 in 292,201,338

    For purposes of planning your future, you can round that number to zero.

    -------------------------------------------

    How about winning the $1 million you get if you get all five numbers without the powerball? The above method is used without the 1:26 thrown in at the end.

    5/69 * 4/68 * 3/67 * 2/66 * 1/65 = 120/1348621560 = 1 in 11,238,513

    -------------------------------------------

    So what are the chances that nobody wins if say 200,000,000 tickets are purchased?
    Well, the chances that a given ticket doesn't win is pretty high. Really high.
    How about 292,201,337 / 292,201,338 which is approximately 0.9999999965777

    The chances that 200,000,000 tickets don't win is this number raised to the 200 millionth power, which turns out to be .504.

    So, even if 200,000,000 tickets are sold, the chances are only about 50:50 that there will be a winner.

    The odds for other numbers of tickets sold are bolow:
    100 million tickets: 71% chance nobody will win.
    200 million tickets: 50% chance nobody will win.
    300 million tickets: 36%
    400 million tickets: 25%
    500 million tickets: 18%
    1 billion tickets:      3% chance nobody will win.