1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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!!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted