You want to calculate your odds at winning the lottery given:

When you select your 1st number, you have 50 numbers to choose from, and...
...a 1 in 50 chance of picking the right one.

(Mathematically, 1 in 50 is represented by the numerical fraction 1/50 or 0.020000.)

When you select your 2nd number, you have 49 numbers to choose from, and...
...a 1 in 49 chance of picking the right one.

(Mathematically, 1 in 49 is represented by the numerical fraction 1/49 or 0.020408.)

When you select your 3rd number, you have 48 numbers to choose from, and...
...a 1 in 48 chance of picking the right one.

(Mathematically, 1 in 48 is represented by the numerical fraction 1/48 or 0.020833.)

When you select your 4th number, you have 47 numbers to choose from, and...
...a 1 in 47 chance of picking the right one.

(Mathematically, 1 in 47 is represented by the numerical fraction 1/47 or 0.021277.)

When you select your 5th number, you have 46 numbers to choose from, and...
...a 1 in 46 chance of picking the right one.

(Mathematically, 1 in 46 is represented by the numerical fraction 1/46 or 0.021739.)

When you select your 6th number, you have 45 numbers to choose from, and...
...a 1 in 45 chance of picking the right one.

(Mathematically, 1 in 45 is represented by the numerical fraction 1/45 or 0.022222.)

In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means to multiply.

So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.

1/50 × 1/49 × 1/48 × 1/47 × 1/46 × 1/45 = 1/11441304000

So, at this point, your odds of winning are 1 in 11441304000. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 6 numbers can be written down, which for 6 numbers is 6! (6 factorial) or 720. Divide 11441304000 by 720 to account for this, to get 15890700.

In other words, there are 720 different ways that the 6 numbers you choose can be filled out on your lottery ticket--if you choose your 6 numbers correctly, any of these ways will make a winning ticket.

That's it! You have a

1 in 15,890,700

chance of winning the lottery you described.

(How do I pronounce this number?)

Here are some other odds for the sake of comparison:
  • You have about a 1 in 2,000,000 chance of being struck by lightning.
  • A pregnant woman has a 1 in 705,000 chance of giving birth to quadruplets.
  • Someone eating an oyster has a 1 in 12,000 chance of finding a pearl inside of it.

Now, lottery odds can be pretty incomprehensible. How can we possibly have any "feeling" for the number 15,890,700? To help you with this, here's a little experiment you can try to "get a handle on" what a 1 in 15,890,700 chance really means.

  1. Get a piece of rope or string, that's 41 feet long.

  2. In a wide open area, arrange the rope or string in a circle, end to end, the best you can.

  3. Get a single grain of sand or dirt (use tweezers!) and place it anywhere you wish inside the circle.

  4. Get a second grain of sand. Close your eyes, and "disorient" yourself as to where the grain of sand is that you placed inside of the circle (have someone spin you around or something!).

  5. While you're inside the circle, drop the second grain of sand from 1 foot up.

  6. Your chances of hitting the first grain of sand with the second is roughly equal to the odds of "1 in 15,890,700."

  7. If the rope's length mentioned in #1 is a little unreasonable, for every foot above the circle that you drop the second grain of sand, you can reduce the length of the string by the same amount. For example, if you dropped the second grain of sand from a ladder 10 feet up, you'd need a length of string that is 10 times shorter than the one in #1, or a 41/10 = 4.10663 foot long piece of string.
Good luck! And sorry to say that the only way to increase your chances of winning is to buy more tickets! Choosing birthdays, your age, addresses, years, phone numbers, etc. does not help at all!