Saturday, April 29, 2023

TI-74 and Python (Casio fx-9750GIII): Probability

TI-74 and Python (Casio fx-9750GIII):  Probability



Today's program illustrates an approach from both the BASIC and Python programming languages. 


The program offers the user to calculate common probability problems:



1)  n!:  factorial of an integer

2)  nCr:  combinations without replacement

3)  nPr:  permutations

4)  nHr:  combinations with replacement

5) bday:  probability that n people do not share a category in common from a size of categories (i.e. birthday problem:  How many people in a room don't share a birthday?)



TI-74 BASICALC Program


200 REM probability

202 INPUT "1)n! 2)nCr 3)nPr 4)nHr 5)bday "; I

204 IF I<5 THEN INPUT "n? "; N

206 IF I>1 AND I<5 THEN INPUT "r? "; R

208 ON I GOTO 220,240,260,280,300


220 X=N

222 GOSUB 320

224 PRINT "n! = "; F: PAUSE

226 GOTO 340


240 Z=1: FOR K=(N-R+1) TO N: Z=Z*K: NEXT K

242 X=R: GOSUB 320

244 Z=Z/F

246 PRINT "nCr = "; Z: PAUSE

248 GOTO 340


260 Z=1: FOR K=(N-R+1) TO N: Z=Z*K: NEXT K

262 PRINT "nPr = "; Z: PAUSE

264 GOTO 340


280 Z=1: FOR K=N TO (N+R-1): Z=Z*K: NEXT K

282 X=R: GOSUB 320: Z=Z/F

284 PRINT "nHr = "; Z: PAUSE

286 GOTO 340


300 INPUT "# categories? "; R

302 INPUT "Sample size? "; N

304 Z=1: FOR K=1 TO (N-1): Z=Z*(1-K/R): NEXT K

306 PRINT "P(all unique) = "; Z: PAUSE

308 GOTO 340


320 F=1

322 FOR K=1 TO X: F=F*K: NEXT K

324 RETURN


340 INPUT "Again? 0:No, 1:Yes "; A

342 IF A=1 THEN 202

344 IF A=0 THEN STOP

346 GOTO 340



Python Program:  prob.py 


Program completed with the Casio fx-9750GIII.


# probability

from math import *


def fact(x):

  f=1

  for k in range(1,x+1):

    f*=k    

  return f



fc=1


while fc!=0:

  print("1)n! 2)nCr")

  print("3)nPr 4)nHr")

  print("5)bday")

  ch=int(input())

  if ch<5:

    n=int(input("n? "))

  if ch>1 and ch<5:

    r=int(input("r? "))

  if ch==1:

    f=fact(n)

    print("n! = "+str(f))

  if ch==2:

    f=fact(n)/(fact(n-r)*fact(r))

    print("nCr = "+str(f))

  if ch==3:

    f=fact(n)/fact(n-r)

    print("nPr = "+str(f))

  if ch==4:

    f=fact(n+r-1)/(fact(r)*fact(n-1))

    print("nHr = "+str(f))

  if ch==5:

    r=int(input("# categories? "))

    n=int(input("Sample size? "))

    f=1

    for k in range(n):

      f*=1-k/r

    print("p(all unique)=")

    print(str(f))

  print("Again? 0)no 1)yes")

  fc=int(input())    


Examples


1) n!  

13! = 6227020800


2) nCr

n = 13, r = 6; result:  1716


3) nPr

n = 13, r = 6; result:  1235520


4) nHr

n = 13, r = 6; result:  18564


5) bday

# categories: 13

Sample size: 6

Result:  P(all unique) = .2559703523



Wishing you an excellent day.   More BASIC and Python programming coming your way tomorrow!


Eddie


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