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Lottery question

  1. Jul 24, 2005 #1
    there is an interesting show i've caught on satellite which is based on a domestic lottery

    you are given the choice of having 100,000 lottery tickets or a $20,000 cash prize

    now to simplify, the odds of matching 3 balls out of 6 is

    ~ 1 in 56.6

    & the prize for matching 3 balls is $10

    if you used a rough calculation, you are likely to win ( just considering 3 balls )

    100,000 *( 1/56.6)* 10 =

    $17,660

    if you took the option of 100,000 tickets


    now, i'm asking what are the precise odds of winning $20,000 ( 2,000 winning "3 ball" tickets ) ?

    i believe it may be something along the lines of


    ( (1/56.6) ^ 2000 ) * (55.6/56.6) ^98000 ) * no. of ways you can ?permute/ ? combine 2000 draws amongst 100,000


    any help would be gratefully appreciated :smile:
     
  2. jcsd
  3. Jul 25, 2005 #2
    That looks right - the binomial term for 2000 successes where the probability p is 1/56.6, normalized by the total number of possibilities.
     
  4. Jul 25, 2005 #3
    I don't get it? Why not 6 choose 3 ways of selecting 3 balls from 6 giving you odds of 1:19?
     
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