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Building a statistical model

  1. Jan 15, 2004 #1
    I have near to no knowledge of statistics, and I want to build a statistical model that can help me calculate %chance of an event happening in situations of type:

    every try has 25% success rate
    after 6 tries, what are the probabilities of having succeeded at least 5times? After 12tries?

    or

    each shot has 42% success rate
    after 5 tries, how what are the probabilities of succeding at least 4times?


    How can I calculate probabilities like these?
     
  2. jcsd
  3. Jan 15, 2004 #2
    Sounds like you want a binomial model. Given probability of success p and n attempts, the probability of exactly k successes is:

    [tex]\binom{n}{k}p^k(1-p)^{n-k}[/tex]

    Of course, to figure out the probability of at least k successes, you have to add up these probabilities for every value greater than or equal to k.
     
  4. Jan 15, 2004 #3
    what does the n above k in brackets mean?
     
  5. Jan 16, 2004 #4

    HallsofIvy

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    [tex]\binom{n}{k}[/tex] is the "binomial coefficient". It is the coefficient of xkyn-k in (x+y)n as well as the kth term in the nth line in Pascal's triangle and can be calculated as [tex]\frac{n!}{k!(n-k)!}[/tex].

    It is sometimes written nCk and our British colleagues seem to refer to it as "n choose k" since it is also the number of different ways one can choose k items from a set of n items.
     
  6. Jan 16, 2004 #5
    And just in case you do not know what [itex]x![/itex] means: it means [itex]x[/itex] factorial:

    [tex]x! = 1\times 2\times 3 \times \ldots \times (x-1) \times x[/tex]
     
  7. Jan 16, 2004 #6
    Ok, thx for explanation!
     
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