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Math Help - lottery question real odds

  1. #1
    Junior Member
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    lottery question real odds

    could someone please help me with this question ?

    a lottery has 45 balls (1 to 45)
    6 balls are randomly generated each week

    you can choose the amount of numbers you want to play
    example
    you can pick 1 number and it pays 6 to 1 if your 1 number comes up in one of the 6
    numbers

    1. question
    I decide to bet 1 on 3 numbers 16 17 23 , which pays 600 to 1 ,
    what are the real odds of hitting all 3 of my numbers and bagging
    600 smackeroons!

    2. what is the ev for this game?

    tx
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  2. #2
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    Quote Originally Posted by jickjoker View Post
    could someone please help me with this question ?

    a lottery has 45 balls (1 to 45)
    6 balls are randomly generated each week

    you can choose the amount of numbers you want to play
    example
    you can pick 1 number and it pays 6 to 1 if your 1 number comes up in one of the 6
    numbers

    1. question
    I decide to bet 1 on 3 numbers 16 17 23 , which pays 600 to 1 ,
    what are the real odds of hitting all 3 of my numbers and bagging
    600 smackeroons!

    2. what is the ev for this game?

    tx
    The probability of hitting all 3 numbers is
    \frac{\binom{42}{3}}{\binom{45}{6}} \approx 0.001409

    The expected value is approximately
    0.001409 \times 600 - 1 = -0.15
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  3. #3
    Junior Member
    Joined
    Sep 2009
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    Since we have 45 unique balls, each time we pick one, the chances of drawing the others increases. So the probability of drawing all three is (3/45) * (2/44) * (1/41). As assuming we pick one of your 3 numbers on the 1st try, we have the other two remaining out of 44.
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