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Math Help - Binomial Distribution in lotto

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by ciaza View Post
    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
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    Thanks you for the help
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