101325__/tex/sh101325wahrscheinlichkeit.txt

ABCD
0101
1001
1000
1111
----- zwischensumme
3213

0100
0111
1001
0001

1101
1100
0000
1000

0101
----- zwischensumme
4515

0000
1110
1001

1101
1110
0100
1100

0001
1001
1111
----- zwischensumme
7635

0110

0001
0010
0001
0010

1001
0000
1010
0000

----- zwischensumme
2143


3   2   1   3
4   5   1   5
7   6   3   5
2   1   4   3
-------------
16  14  9   16

absolute wahrscheinlichkeit

H_a = 16
H_b = 14
H_c = 9
H_d = 16
n = 32

h(E) = H/n

h(A) = H_a/n = 16/32 = 0.5
h(B) = H_b/n = 14/32 = 0.4375
h(C) = H_c/n = 9/32 = 0.28125
h(D) = H_d/n = 16/32 = 0.5
man sage ueber die ziffern, welche in welches Ereignis passt

Ereignis E = {ABD} = {H_a = 16, H_b = 14, H_d = 16, n = 32*3}, h(E) = (16+14+16)/(32*3)
Ereignis F = {BD} = {H_b = 14, H_d = 16, n = 32*2}, h(F) = (14+16)/(32*2)
Ereignis G = {AC} = {H_a = 16, H_c = 9, n = 32*2}, h(G) = (16+9)/(32*2)
Ereignis H = {D} = {H_d = 16, n = 32}, h(H) = (16/32)
Ereignis I = {ABC} = {H_a = 16, H_b = 14, H_c = 9, n = 32*3}, h(I) = (16+14+9)/(32*3)

in python3

# (c) david vajda
# wahrscheinlichkeitsausrechnung
# 13/10/25

print ("h(E) = ", (16+14+16)/(32*3))
print ("h(F) = ", (14+16)/(32*2))
print ("h(G) = ", (16+9)/(32*2))
print ("h(H) = ", (16/32))
print ("h(I) = ", (16+14+9)/(32*3))

h(A) = H_a/n = 16/32 = 0.5
h(B) = H_b/n = 14/32 = 0.4375
h(C) = H_c/n = 9/32 = 0.28125
h(D) = H_d/n = 16/32 = 0.5
h(E) =  0.4791666666666667
h(F) =  0.46875
h(G) =  0.390625
h(H) =  0.5
h(I) =  0.40625


h(A) = 0.5
h(B) = 0.4375
h(C) = 0.28125
h(D) = 0.5
h(E) = 0.4791666666666667
h(F) = 0.46875
h(G) = 0.390625
h(H) = 0.5
h(I) = 0.40625

beruehmte tabelle:


   in prozent                   in prozent ist
   ist eingetreten              nicht eingetreten
   relative haeufigkeit         relative haeufigkeit
A       0.5                         0.5
B       0.4375                      0.5625
C       0.28125                     0.71875
D       0.5                         0.5
E       0.4791666666666667          0.5208333333333333
F       0.46875                     0.53125
G       0.390625                    0.609375
H       0.5                         0.5
I       0.40625                     0.59375


0.5
0.5625
0.71875
0.5
0.5208333333333333
0.53125
0.609375
0.5
0.59375


print(1-0.5)
print(1-0.4375)
print(1-0.28125)
print(1-0.5)
print(1-0.4791666666666667)
print(1-0.46875)
print(1-0.390625)
print(1-0.5)
print(1-0.40625)