Posted by **Anonymous** on Sunday, December 1, 2013 at 8:35pm.

A certain state's lottery game, LOTTO, is set up so that each player pays $1 per ticket and chooses six different numbers between 1 and 20 inclusive. If the six numbers chosen match the six numbers drawn, the player wins the grand prize.

If a person buys one LOTTO ticket, what is his probability of winning the grand price?

- Math Probability -
**Joe**, Sunday, December 1, 2013 at 8:53pm
20 x 20 x 20 x 20 x 20 x 20

You have 20 chances for each number and that happens for each draw...

you have 1 chance out of _________

Can you finish from here?

- Math Probability -
**Reiny**, Sunday, December 1, 2013 at 9:02pm
Joe has assumed that the same number could be drawn more than once.

However,in most of these lotteries, some kind of drawing method is used, such as 20 different-numbered pingpong balls, and the order that they are drawn does not matter.

Number of ways to draw 6 numbers from 20

is C(20,6) = 38760

so prob(winner) = 1/38760

- Math Probability -
**Anonymous**, Sunday, December 1, 2013 at 9:09pm
Thank You, Joe and Reiny for your help. I believe Reiny you use combination formula and I believe you are right, because the question does states that the order doesn't matter. Once again thanks to you both

- Math Probability -
**Tina**, Sunday, December 1, 2013 at 10:24pm
I decided to add my name. This is my first time on here and I wanted to see what its all about...

another question I'm struggling with

If a person buys 1000 LOTTO tickets, what is his probability of winning the grand prize?

- Math Probability -
**Anonymous**, Monday, June 2, 2014 at 10:20pm
Assuming that you don't play the same set of numbers and it is the same drawing. All you do is add the number of tickets bought to the top number so 1000/38760. Which is about a 2.5% chance of winning. If it is one ticket a game for a 1000 times. It stays 1/38760.

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