(11C) Probability of No Repetitions

[Gamo]

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

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:


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