(11C) Probability of No Repetitions
01-10-2020, 12:42 PM (This post was last modified: 01-11-2020 01:02 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 702 Joined: Dec 2016
(11C) Probability of No Repetitions
This program was adapted from HP-55 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- (n-1/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: HP-55 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

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:
 LBL A  // m STO 1 RTN LBL B  // n STO 2 1 STO 0 LBL 0 RCL 1 RCL 2 1 - STO 2 0 X=Y GTO 1 Rv X<>Y ÷ 1 X<>Y - STOx0 GTO 0 LBL 1 RCL 0 PSE 1 RCL 0 RND - EEX 2 x RTN

Gamo 1/2020
 « Next Oldest | Next Newest »

 Messages In This Thread (11C) Probability of No Repetitions - Gamo - 01-10-2020 12:42 PM RE: (11C) Probability of No Repetitions - Albert Chan - 01-11-2020, 01:46 AM RE: (11C) Probability of No Repetitions - Albert Chan - 01-11-2020, 02:15 PM

User(s) browsing this thread: 1 Guest(s)