vier_oder_acht

probability
Published

November 20, 2025

1 Aufgabe

Sie werfen eine (faire) Münze acht Mal.

Welches Ergebnis ist am wahrscheinlichsten?

  1. 4 Mal Kopf ist am wahrscheinlichsten
  2. 8 Mal Kopf ist am wahrscheinlichsten
  3. Beide Ereignisse (4 Mal bzw. 8 Mal Kopf) sind gleich wahrscheinlich.
  4. Keine Aussage möglich.













2 Lösung

4 Mal Kopf ist wahrscheinlicher als 8 Mal Kopf.

Hier sind alle möglichen Ereignisse dieses Zufallsexperiments:

Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 event heads_n
H H H H H H H H HHHHHHHH 8
T H H H H H H H THHHHHHH 7
H T H H H H H H HTHHHHHH 7
T T H H H H H H TTHHHHHH 6
H H T H H H H H HHTHHHHH 7
T H T H H H H H THTHHHHH 6
H T T H H H H H HTTHHHHH 6
T T T H H H H H TTTHHHHH 5
H H H T H H H H HHHTHHHH 7
T H H T H H H H THHTHHHH 6
H T H T H H H H HTHTHHHH 6
T T H T H H H H TTHTHHHH 5
H H T T H H H H HHTTHHHH 6
T H T T H H H H THTTHHHH 5
H T T T H H H H HTTTHHHH 5
T T T T H H H H TTTTHHHH 4
H H H H T H H H HHHHTHHH 7
T H H H T H H H THHHTHHH 6
H T H H T H H H HTHHTHHH 6
T T H H T H H H TTHHTHHH 5
H H T H T H H H HHTHTHHH 6
T H T H T H H H THTHTHHH 5
H T T H T H H H HTTHTHHH 5
T T T H T H H H TTTHTHHH 4
H H H T T H H H HHHTTHHH 6
T H H T T H H H THHTTHHH 5
H T H T T H H H HTHTTHHH 5
T T H T T H H H TTHTTHHH 4
H H T T T H H H HHTTTHHH 5
T H T T T H H H THTTTHHH 4
H T T T T H H H HTTTTHHH 4
T T T T T H H H TTTTTHHH 3
H H H H H T H H HHHHHTHH 7
T H H H H T H H THHHHTHH 6
H T H H H T H H HTHHHTHH 6
T T H H H T H H TTHHHTHH 5
H H T H H T H H HHTHHTHH 6
T H T H H T H H THTHHTHH 5
H T T H H T H H HTTHHTHH 5
T T T H H T H H TTTHHTHH 4
H H H T H T H H HHHTHTHH 6
T H H T H T H H THHTHTHH 5
H T H T H T H H HTHTHTHH 5
T T H T H T H H TTHTHTHH 4
H H T T H T H H HHTTHTHH 5
T H T T H T H H THTTHTHH 4
H T T T H T H H HTTTHTHH 4
T T T T H T H H TTTTHTHH 3
H H H H T T H H HHHHTTHH 6
T H H H T T H H THHHTTHH 5
H T H H T T H H HTHHTTHH 5
T T H H T T H H TTHHTTHH 4
H H T H T T H H HHTHTTHH 5
T H T H T T H H THTHTTHH 4
H T T H T T H H HTTHTTHH 4
T T T H T T H H TTTHTTHH 3
H H H T T T H H HHHTTTHH 5
T H H T T T H H THHTTTHH 4
H T H T T T H H HTHTTTHH 4
T T H T T T H H TTHTTTHH 3
H H T T T T H H HHTTTTHH 4
T H T T T T H H THTTTTHH 3
H T T T T T H H HTTTTTHH 3
T T T T T T H H TTTTTTHH 2
H H H H H H T H HHHHHHTH 7
T H H H H H T H THHHHHTH 6
H T H H H H T H HTHHHHTH 6
T T H H H H T H TTHHHHTH 5
H H T H H H T H HHTHHHTH 6
T H T H H H T H THTHHHTH 5
H T T H H H T H HTTHHHTH 5
T T T H H H T H TTTHHHTH 4
H H H T H H T H HHHTHHTH 6
T H H T H H T H THHTHHTH 5
H T H T H H T H HTHTHHTH 5
T T H T H H T H TTHTHHTH 4
H H T T H H T H HHTTHHTH 5
T H T T H H T H THTTHHTH 4
H T T T H H T H HTTTHHTH 4
T T T T H H T H TTTTHHTH 3
H H H H T H T H HHHHTHTH 6
T H H H T H T H THHHTHTH 5
H T H H T H T H HTHHTHTH 5
T T H H T H T H TTHHTHTH 4
H H T H T H T H HHTHTHTH 5
T H T H T H T H THTHTHTH 4
H T T H T H T H HTTHTHTH 4
T T T H T H T H TTTHTHTH 3
H H H T T H T H HHHTTHTH 5
T H H T T H T H THHTTHTH 4
H T H T T H T H HTHTTHTH 4
T T H T T H T H TTHTTHTH 3
H H T T T H T H HHTTTHTH 4
T H T T T H T H THTTTHTH 3
H T T T T H T H HTTTTHTH 3
T T T T T H T H TTTTTHTH 2
H H H H H T T H HHHHHTTH 6
T H H H H T T H THHHHTTH 5
H T H H H T T H HTHHHTTH 5
T T H H H T T H TTHHHTTH 4
H H T H H T T H HHTHHTTH 5
T H T H H T T H THTHHTTH 4
H T T H H T T H HTTHHTTH 4
T T T H H T T H TTTHHTTH 3
H H H T H T T H HHHTHTTH 5
T H H T H T T H THHTHTTH 4
H T H T H T T H HTHTHTTH 4
T T H T H T T H TTHTHTTH 3
H H T T H T T H HHTTHTTH 4
T H T T H T T H THTTHTTH 3
H T T T H T T H HTTTHTTH 3
T T T T H T T H TTTTHTTH 2
H H H H T T T H HHHHTTTH 5
T H H H T T T H THHHTTTH 4
H T H H T T T H HTHHTTTH 4
T T H H T T T H TTHHTTTH 3
H H T H T T T H HHTHTTTH 4
T H T H T T T H THTHTTTH 3
H T T H T T T H HTTHTTTH 3
T T T H T T T H TTTHTTTH 2
H H H T T T T H HHHTTTTH 4
T H H T T T T H THHTTTTH 3
H T H T T T T H HTHTTTTH 3
T T H T T T T H TTHTTTTH 2
H H T T T T T H HHTTTTTH 3
T H T T T T T H THTTTTTH 2
H T T T T T T H HTTTTTTH 2
T T T T T T T H TTTTTTTH 1
H H H H H H H T HHHHHHHT 7
T H H H H H H T THHHHHHT 6
H T H H H H H T HTHHHHHT 6
T T H H H H H T TTHHHHHT 5
H H T H H H H T HHTHHHHT 6
T H T H H H H T THTHHHHT 5
H T T H H H H T HTTHHHHT 5
T T T H H H H T TTTHHHHT 4
H H H T H H H T HHHTHHHT 6
T H H T H H H T THHTHHHT 5
H T H T H H H T HTHTHHHT 5
T T H T H H H T TTHTHHHT 4
H H T T H H H T HHTTHHHT 5
T H T T H H H T THTTHHHT 4
H T T T H H H T HTTTHHHT 4
T T T T H H H T TTTTHHHT 3
H H H H T H H T HHHHTHHT 6
T H H H T H H T THHHTHHT 5
H T H H T H H T HTHHTHHT 5
T T H H T H H T TTHHTHHT 4
H H T H T H H T HHTHTHHT 5
T H T H T H H T THTHTHHT 4
H T T H T H H T HTTHTHHT 4
T T T H T H H T TTTHTHHT 3
H H H T T H H T HHHTTHHT 5
T H H T T H H T THHTTHHT 4
H T H T T H H T HTHTTHHT 4
T T H T T H H T TTHTTHHT 3
H H T T T H H T HHTTTHHT 4
T H T T T H H T THTTTHHT 3
H T T T T H H T HTTTTHHT 3
T T T T T H H T TTTTTHHT 2
H H H H H T H T HHHHHTHT 6
T H H H H T H T THHHHTHT 5
H T H H H T H T HTHHHTHT 5
T T H H H T H T TTHHHTHT 4
H H T H H T H T HHTHHTHT 5
T H T H H T H T THTHHTHT 4
H T T H H T H T HTTHHTHT 4
T T T H H T H T TTTHHTHT 3
H H H T H T H T HHHTHTHT 5
T H H T H T H T THHTHTHT 4
H T H T H T H T HTHTHTHT 4
T T H T H T H T TTHTHTHT 3
H H T T H T H T HHTTHTHT 4
T H T T H T H T THTTHTHT 3
H T T T H T H T HTTTHTHT 3
T T T T H T H T TTTTHTHT 2
H H H H T T H T HHHHTTHT 5
T H H H T T H T THHHTTHT 4
H T H H T T H T HTHHTTHT 4
T T H H T T H T TTHHTTHT 3
H H T H T T H T HHTHTTHT 4
T H T H T T H T THTHTTHT 3
H T T H T T H T HTTHTTHT 3
T T T H T T H T TTTHTTHT 2
H H H T T T H T HHHTTTHT 4
T H H T T T H T THHTTTHT 3
H T H T T T H T HTHTTTHT 3
T T H T T T H T TTHTTTHT 2
H H T T T T H T HHTTTTHT 3
T H T T T T H T THTTTTHT 2
H T T T T T H T HTTTTTHT 2
T T T T T T H T TTTTTTHT 1
H H H H H H T T HHHHHHTT 6
T H H H H H T T THHHHHTT 5
H T H H H H T T HTHHHHTT 5
T T H H H H T T TTHHHHTT 4
H H T H H H T T HHTHHHTT 5
T H T H H H T T THTHHHTT 4
H T T H H H T T HTTHHHTT 4
T T T H H H T T TTTHHHTT 3
H H H T H H T T HHHTHHTT 5
T H H T H H T T THHTHHTT 4
H T H T H H T T HTHTHHTT 4
T T H T H H T T TTHTHHTT 3
H H T T H H T T HHTTHHTT 4
T H T T H H T T THTTHHTT 3
H T T T H H T T HTTTHHTT 3
T T T T H H T T TTTTHHTT 2
H H H H T H T T HHHHTHTT 5
T H H H T H T T THHHTHTT 4
H T H H T H T T HTHHTHTT 4
T T H H T H T T TTHHTHTT 3
H H T H T H T T HHTHTHTT 4
T H T H T H T T THTHTHTT 3
H T T H T H T T HTTHTHTT 3
T T T H T H T T TTTHTHTT 2
H H H T T H T T HHHTTHTT 4
T H H T T H T T THHTTHTT 3
H T H T T H T T HTHTTHTT 3
T T H T T H T T TTHTTHTT 2
H H T T T H T T HHTTTHTT 3
T H T T T H T T THTTTHTT 2
H T T T T H T T HTTTTHTT 2
T T T T T H T T TTTTTHTT 1
H H H H H T T T HHHHHTTT 5
T H H H H T T T THHHHTTT 4
H T H H H T T T HTHHHTTT 4
T T H H H T T T TTHHHTTT 3
H H T H H T T T HHTHHTTT 4
T H T H H T T T THTHHTTT 3
H T T H H T T T HTTHHTTT 3
T T T H H T T T TTTHHTTT 2
H H H T H T T T HHHTHTTT 4
T H H T H T T T THHTHTTT 3
H T H T H T T T HTHTHTTT 3
T T H T H T T T TTHTHTTT 2
H H T T H T T T HHTTHTTT 3
T H T T H T T T THTTHTTT 2
H T T T H T T T HTTTHTTT 2
T T T T H T T T TTTTHTTT 1
H H H H T T T T HHHHTTTT 4
T H H H T T T T THHHTTTT 3
H T H H T T T T HTHHTTTT 3
T T H H T T T T TTHHTTTT 2
H H T H T T T T HHTHTTTT 3
T H T H T T T T THTHTTTT 2
H T T H T T T T HTTHTTTT 2
T T T H T T T T TTTHTTTT 1
H H H T T T T T HHHTTTTT 3
T H H T T T T T THHTTTTT 2
H T H T T T T T HTHTTTTT 2
T T H T T T T T TTHTTTTT 1
H H T T T T T T HHTTTTTT 2
T H T T T T T T THTTTTTT 1
H T T T T T T T HTTTTTTT 1
T T T T T T T T TTTTTTTT 0

Hier sind alle Ereignisse mit 4 Treffern (Kopf):

Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 event heads_n
T T T T H H H H TTTTHHHH 4
T T T H T H H H TTTHTHHH 4
T T H T T H H H TTHTTHHH 4
T H T T T H H H THTTTHHH 4
H T T T T H H H HTTTTHHH 4
T T T H H T H H TTTHHTHH 4
T T H T H T H H TTHTHTHH 4
T H T T H T H H THTTHTHH 4
H T T T H T H H HTTTHTHH 4
T T H H T T H H TTHHTTHH 4
T H T H T T H H THTHTTHH 4
H T T H T T H H HTTHTTHH 4
T H H T T T H H THHTTTHH 4
H T H T T T H H HTHTTTHH 4
H H T T T T H H HHTTTTHH 4
T T T H H H T H TTTHHHTH 4
T T H T H H T H TTHTHHTH 4
T H T T H H T H THTTHHTH 4
H T T T H H T H HTTTHHTH 4
T T H H T H T H TTHHTHTH 4
T H T H T H T H THTHTHTH 4
H T T H T H T H HTTHTHTH 4
T H H T T H T H THHTTHTH 4
H T H T T H T H HTHTTHTH 4
H H T T T H T H HHTTTHTH 4
T T H H H T T H TTHHHTTH 4
T H T H H T T H THTHHTTH 4
H T T H H T T H HTTHHTTH 4
T H H T H T T H THHTHTTH 4
H T H T H T T H HTHTHTTH 4
H H T T H T T H HHTTHTTH 4
T H H H T T T H THHHTTTH 4
H T H H T T T H HTHHTTTH 4
H H T H T T T H HHTHTTTH 4
H H H T T T T H HHHTTTTH 4
T T T H H H H T TTTHHHHT 4
T T H T H H H T TTHTHHHT 4
T H T T H H H T THTTHHHT 4
H T T T H H H T HTTTHHHT 4
T T H H T H H T TTHHTHHT 4
T H T H T H H T THTHTHHT 4
H T T H T H H T HTTHTHHT 4
T H H T T H H T THHTTHHT 4
H T H T T H H T HTHTTHHT 4
H H T T T H H T HHTTTHHT 4
T T H H H T H T TTHHHTHT 4
T H T H H T H T THTHHTHT 4
H T T H H T H T HTTHHTHT 4
T H H T H T H T THHTHTHT 4
H T H T H T H T HTHTHTHT 4
H H T T H T H T HHTTHTHT 4
T H H H T T H T THHHTTHT 4
H T H H T T H T HTHHTTHT 4
H H T H T T H T HHTHTTHT 4
H H H T T T H T HHHTTTHT 4
T T H H H H T T TTHHHHTT 4
T H T H H H T T THTHHHTT 4
H T T H H H T T HTTHHHTT 4
T H H T H H T T THHTHHTT 4
H T H T H H T T HTHTHHTT 4
H H T T H H T T HHTTHHTT 4
T H H H T H T T THHHTHTT 4
H T H H T H T T HTHHTHTT 4
H H T H T H T T HHTHTHTT 4
H H H T T H T T HHHTTHTT 4
T H H H H T T T THHHHTTT 4
H T H H H T T T HTHHHTTT 4
H H T H H T T T HHTHHTTT 4
H H H T H T T T HHHTHTTT 4
H H H H T T T T HHHHTTTT 4

Hier sind alle Ereignisse mit 8 Treffern (Kopf):

Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 event heads_n
H H H H H H H H HHHHHHHH 8

Es gibt also sehr viel mehr Möglichkeiten (Elementarereignisse, Ergebnisse), 4 Treffer zu erzielen als 8 Treffer.

Da alle Elementarereignisse gleich wahrscheinlisch sind, ist das Ereignis “4 Treffer” wahrscheinlicher als das Ereignis “8 Treffer”.