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Theoretical probabilities in Bernoulli trials

Beginning status (before activations):

   1 *
   2 *A random variable Y has a Bernoulli(p) distribution if
   3 *         1 with probability p
   4 *   Y  =                            , 0 <= p <= 1 .
   5 *         0 with probability 1 - p
   6 *Define the events
   7 *   Ai = { Y = 1 on the i'th trial },  i = 1, 2, ..., N.
   8 *In the following, we assume that the events A1, ..., AN are
   9 *a collection of independent events.
  10 *   Assume that we have N=13 trials and in each one the success
  11 *probability is p=1/3. The probability of having at least 10
  12 *successes is obtained from the binomial distribution function
  13 *
  14 *   1-BIN.F(N,p,9)=                 (i.e. more than 9 successes)
  15 *
  16 *The same result is achieved with binomial coefficients C(n,m) by
  17 *defining a temporary F function:
  18 *
  19 *   F(N,p,X):=for(i=0)to(X)sum(C(N,i)*p^i*(1-p)^(N-i))
  20 * 1-F(N,p,9)=  
  21 *

Ending status (after activations):

   1 *
   2 *A random variable Y has a Bernoulli(p) distribution if
   3 *         1 with probability p
   4 *   Y  =                            , 0 <= p <= 1 .
   5 *         0 with probability 1 - p
   6 *Define the events
   7 *   Ai = { Y = 1 on the i'th trial },  i = 1, 2, ..., N.
   8 *In the following, we assume that the events A1, ..., AN are
   9 *a collection of independent events.
  10 *   Assume that we have N=13 trials and in each one the success
  11 *probability is p=1/3. The probability of having at least 10
  12 *successes is obtained from the binomial distribution function
  13 *
  14 *   1-BIN.F(N,p,9)=0.00164772132121 (i.e. more than 9 successes)
  15 *
  16 *The same result is achieved with binomial coefficients C(n,m) by
  17 *defining a temporary F function:
  18 *
  19 *   F(N,p,X):=for(i=0)to(X)sum(C(N,i)*p^i*(1-p)^(N-i))
  20 * 1-F(N,p,9)=0.00164772132121
  21 *

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