# Thread: Binomial Distribution in lotto

1. ## Binomial Distribution in lotto

Hey guys, first-time poster. I'm having particular difficulty with a question given in class, and my teacher is not very helpful.

Your chance of winning on one game in Tattslotto is 1/8150000. You purchase sufficient tickets to ensure a 50% chance of winning at least once and there are 16 games on each ticket. The cost of each ticket is $5.10 and the maximum amount possible to win is$1 000 000. Use Binary Distribution to decide if you come out on front in your investment.

I worked it out using logic but got a different answer using binary distribution. Can someone please help?

2. Originally Posted by ciaza
Hey guys, first-time poster. I'm having particular difficulty with a question given in class, and my teacher is not very helpful.

Your chance of winning on one game in Tattslotto is 1/8150000. You purchase sufficient tickets to ensure a 50% chance of winning at least once and there are 16 games on each ticket. The cost of each ticket is $5.10 and the maximum amount possible to win is$1 000 000. Use Binary Distribution to decide if you come out on front in your investment.

I worked it out using logic but got a different answer using binary distribution. Can someone please help?
If you buy $n$ games the probability that they all lose is:

$pr=(1-p)^n$

where $p$ is the probability that a single game wins.

So the number of games required so that the probability of one or more wins is greater then $0.5$ is the smallest integer $n$ greater than:

$x=\dfrac{\ln(0.5)}{\ln(1-p)}$

Now you need to turn this into a number of tickets, and so a cost.

Now you need to work out your expected return (which will be $(n/8150000)1000000$ )

CB

3. Thanks you for the help