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Bingo Game Probability

  1. May 15, 2014 #1
    Hey all,
    have a problem to solve for my new game game. really appreciate if someone can help me solve this issue:

    * i need to calculate the probability for a given combination


    1. Total number of balls in the box = 80
    2. Total number of chosen balls 45
    3. for simplicity we have only 1 card 5x5 (25 numbers in total)


    question
    what is the probability that i will get
    a. 4 corners of the card?
    b. any row ?
    c. any 2 rows?

    if someone can give me a start i will be happy
     
  2. jcsd
  3. May 16, 2014 #2
    Here's a start. I'm assuming you are holding the card and the 4 corners are known. There are C(80,45) possible combinations of 45 drawn from 80. There are C(76,41) combinations that contain your 4 corners so the probability of getting all 4 corners is C(76,41)/C(80,45). Any row is similar except that there are 5 of them, each containing 5 numbers. Give it a try.
     
  4. May 17, 2014 #3

    thank you very much. for the rows because i can get 5 different combination

    (c(76,41)/c(80,45))*5

    is that correct?

    i assume not cause it includes the probability of getting 2 rows together or 3 rows or 4 rows, right?
     
  5. May 18, 2014 #4
    is this the correct answer for 'any row'

    (c(76,41)/c(80,45))*5 - ( (c(76,41)/c(80,45))^5 + (c(76,41)/c(80,45))^4 + (c(76,41)/c(80,45))^3 + (c(76,41)/c(80,45))^2 )

    so change of getting a row multiply by 5 = this will give me the chance of geting 1st OR 2nd OR 3th OR 4th OR 5th

    but will also give me AND 5,4,3,2 rows together - there for i deduct those
     
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