(11C) Probability of No Repetitions

01102020, 12:42 PM
(This post was last modified: 01112020 01:02 AM by Gamo.)
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(11C) Probability of No Repetitions
This program was adapted from HP55 Statistic Book (Page 12)
Reference: E. Parzen, Modern Probability Theory and its Applications, John Wiley and Sons, 1960 (CH. 2 Page 46) As stated in the book: Probability of No Repetitions in a Sample Suppose a sample of size n is drawn with replacement from population containing m different objects. Let P be the probability that there are no repetitions in the sample, then P = [1 (1/m)][1 (2/m)]....[1 (n1/m)] Given integer m, n such that m ≥ n ≥ 1 this program finds the probability P. Remark: The execution time of the program depends on n; the larger n is, the longer it takes.  Example: HP55 Statistic Book page 13 In a room containing n persons, what is the probability that no two or more persons have the same birthday for n = 4, 23, 48? Note: m = 365 // 365 is the days amount of birthday [USER] [FIX] 2 365 [A] display 365.00 // Enter m 4 [B] display brieftly 0.98 then 2.00 // Enter n 23 [B] display briefly 0.49 the 51.00 48 [B] display briefly 0.04 then 96.00 Answer: In a room for the probability that at lease two of them will have the same birthday 4 people in a room P = 0.98 or only 2% 23 people in a room P = 0.49 or 51% 48 people in a room P = 0.04 or 96%  Program: Code:
Gamo 1/2020 

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(11C) Probability of No Repetitions  Gamo  01102020 12:42 PM
RE: (11C) Probability of No Repetitions  Albert Chan  01112020, 01:46 AM
RE: (11C) Probability of No Repetitions  Albert Chan  01112020, 02:15 PM

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