Math/Lottery Question?

Question

I need help with a math question to settle a debate.

To win the lottery you need to have 5 out of 5 numbers drawn. The numbers
range from 1-59. There is a bonus number drawn.

What are the odds of winning based off of playing ONE game?
What are the odds of winning based off of playing 500 games?
What are the odds of winning based off of playing 1000 games?

Thanks!

Answer 1

If we are talking about probabilities, here is how you break down: To guess a number right, you will have 1/59 of chance or, 1.7 %. To get 5 numbers straight, you would need (1/59)*(1/59)*(1/59)*(1/59)*(1/59), or (1/59)^6 = 1.38 x 10^-9 or 1.38 out of one billion. Factoring in the bonus number, or another multiplication of (1/59), it will be 0.024 out of a billion. This is for one game only.

If 500 games are played, 699 and 11.9 out of one billion chances for 5 numbers and 5 numbers plus one bonus number respectively. If 1000 games are played, it's 1399 and 23.7 out of one billion.


XR

Answer 2

The odds of getting 5-of-5 in a 5/59 game are
if you play 1 game --- 1 in 5,006,386
if you play 500 games --- 1 in 10,013
if you play 1000 games --- 1 in 5,006

The bonus number is always drawn from the same lot, therefore it doesn't play a role in calculating the odds. Also, it is used for lower prizes and not for the jackpot.

You can find an odds calculator for any lottery game at http://www.betstarter.com/lottery/LottoOdds.asp

Answer 3

Use combinations (nCr) on your calc
59 nCr 5 this means out of 59 numbers choose 5. Then after that you need to multiply by however numbers are in the bonus number bin.

1 chance
-------
(59nCr5 * 59) if we assume the bonus number can be out of 59


Second 500/(59nCr5 * 59)

Third 1000/(59nCr5 * 59)

I don't have my calc on me right now, so you will have to work out the 59nCr5