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In probability formula, what does n represent?

  1. Mar 24, 2013 #1
    In the formula,

    PN(n) = N!/(n!(N-N)!) (p^n)(q^(N-n))

    N represents the number of elements, but what exactly does little n represent?

    Thanks for any help!
     
  2. jcsd
  3. Mar 24, 2013 #2

    CompuChip

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    The formula you gave,
    [tex]P_N(n) = \frac{N!}{n! (N - n)!} p^n q^{N - n}[/tex]
    is the probability of n successes after N trials in a binomial distribution.

    That is, you run N trials and for each of them the chance for "success" is p, and the chance for "failure" is q = 1 - p. The formula above gives the probability that out of the N trials, you get [itex]0 \le n \le N[/itex] "successes".

    Some examples: if you flip a coin N times, and define "success" as "heads comes up" (with p = 1/2) then PN(n) is the probability of finding exactly n heads and N - n tails in N flips.

    If you throw a die N times, and define "success" as "six comes up" (with p = 1/6) then PN(n) is the probability of getting exactly n sixes and N - n other values in N throws.

    If a multiple-choice exam has N questions, and you randomly select one of the four answers for each of them then "success" can be "question is answered correctly" (with p = 1/4) and PN(n) is the probability of getting exactly n questions right and N - n wrong.
     
  4. Mar 24, 2013 #3
    This helps so much! Thank you!!
     
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