F:\O\_Mathematik\Material\Stochstik\Geogebra\MehrstufigeZE\baum_mensch2

Wdh: n

P(R_1) =

tR1f =

B: \text{erkrankte Person}

\overline{B}: \text{gesunde Person}

A: \text{positives Testergebnis}

\overline{A}: \text{negatives Testergebnis}

A

B

\overline{B}

\overline{A}

P_{A}(B) =

P_{\overline{A}}(B) =

P_{A}(\overline{B}) =

P_{\overline{A}}(\overline{B}) =

P(A) =

P(\overline{A}) =

P(A|B) = 

P_{B}(\overline{A}) = 

P(A|\overline{B}) = 

P(\overline{A}|B) = 

P(\overline{A}|\overline{B}) = 

P(B) = 

P(\overline{B}) = 

n =

Häufigkeiten

Lösungen

P(B \cap A) = 

P(B \cap \overline{A}) = 

P(\overline{B} \cap A) = 

P(\overline{B} \cap \overline{A}) = 

H(B \cap A) = 

H(B \cap \overline{A}) = 

H(\overline{B} \cap A) = 

H(\overline{B} \cap \overline{A}) = 

H(B) = 

H(\overline{B}) = 

H(A) = 

H(\overline{A}) = 

h(B|A) = 

h(B|\overline{A}) = 

h(\overline{B}|A) = 

h(\overline{B}|\overline{A}) = 

Wahrscheinlichkeiten

xBw = 0.2 (slider from -5 to 5, step 0.1)
xBfAf = 0.8 (slider from -5 to 5, step 0.1)
xBfAw: 1 - xBfAf
xBf: 1 - xBw
pBfAf: (xBf * xBfAf)
pBfAw: (xBf * xBfAw)
xBwAw = 0.9 (slider from -5 to 5, step 0.1)
pBwAw: (xBw * xBwAw)
xBwAf: 1 - xBwAw
pBwAf: (xBw * xBwAf)
korrekturPosE: (1, 0)
korrekturV: (-1, 0.5)
av3 = 0.2 (slider from -5 to 5, step 0.1)
av2 = 2.3 (slider from -5 to 5, step 0.1)
av1 = 2.9 (slider from -5 to 5, step 0.1)
av: (av1, av2, av3)
ah3 = 0.9 (slider from -5 to 5, step 0.1)
ah2 = 4.7 (slider from -5 to 5, step 0.1)
ah1 = 4.7 (slider from -5 to 5, step 0.1)
ah: (ah1, ah2, ah3)
struktur: {{"O", (0 | 0 | 0), (0 | 0 | 0), "P(B) = 0.4", "B", (1 | 0 | 0), (1 | 0 | 0), 1}, {"O", (1 | 0 | 0), (1 | 0 | 0), "P_{B}(A) = 0.25", "A", (2 | 0 | 0), (1 | 1 | 0), 2}, {"O", (1 | 0 | 0), (1 | 0 | 0), "P_{B}(\overline{A}) = 0.75", "\overline{A}", (2 | 0 | 0), (1 | -1 | 0), 2}, {"O", (0 | 0 | 0), (0 | 0 | 0), "P(\overline{B}) = 0.6", "\overline{B}", (1 | 0 | 0), (-1 | 0 | 0), 1}, {"O", (1 | 0 | 0), (-1 | 0 | 0), "P_{\overline{B}}(A) = 0.5", "A", (2 | 0 | 0), (-1 | 1 | 0), 2}, {"O", (1 | 0 | 0), (-1 | 0 | 0), "P_{\overline{B}}(\overline{A}) = 0.5", "\overline{A}", (2 | 0 | 0), (-1 | -1 | 0), 2}}
stufe = 2 (slider from 0 to 2, step 1)
verbindungen = Sequence(If[Element[Element[struktur, i], 8] ≤ stufe, Segment[((Element[Element[struktur, i], 2] * ah) | (Element[Element[struktur, i], 3] * av)), ((Element[Element[struktur, i], 6] * ah) | (Element[Element[struktur, i], 7] * av))]], i, 1, Length[struktur])
verbindungsmitten = Zip(Midpoint[S], S, verbindungen)
positionWahrscheinlichkeiten = Sequence(Element[verbindungsmitten, i] + korrekturV, i, 1, Length[verbindungsmitten])
korrekturW: (4, 0.3)
positionenTabelle = Sequence((((1 | 1 | 1) * ah) | (Element[Element[struktur, i], 7] * av)), i, 1, Length[struktur])
korrekturWB: (3.5, 0.3)
korrekturE: (0.5, 0.3)
positionenWBerechnet = Sequence(Element[positionenTabelle, i] + korrekturWB, i, 1, Length[positionenTabelle])
positionenElemente = Sequence(Element[positionenTabelle, i] + korrekturE, i, 1, Length[positionenTabelle])
hBaum = Max(Sequence[y(Element[positionenElemente, i]), i, 1, Length[positionenElemente]])
anzahlWdh = 2160 (slider from 0 to 2160, step 216)
tabelle: {{false, "A", "\frac{1}{2}", 0}, {true, "B \cap A = \{RR\}", LaTeX[pBwAw], 1}, {true, "B \cap \overline{A} = \{RB\}", LaTeX[pBwAf], 1}, {false, "C", "\frac{1}{4}", 0}, {true, "\overline{B} \cap A = \{BR\}", LaTeX[pBfAw], 1}, {true, "\overline{B} \cap \overline{A} = \{BB\}", LaTeX[pBfAf], 1}}
r = 0.4 (slider from -5 to 5, step 0.1)
I2 = NaN
knotenmitten = Sequence(If[Element[Element[struktur, i], 8] ≤ stufe, ((Element[Element[struktur, i], 6] * ah) | (Element[Element[struktur, i], 7] * av))], i, 1, Length[struktur])
knoten = Zip(Circle[X, r], X, knotenmitten)
wahrscheinlichkeiten = Sequence(Element[Element[struktur, i], 4], i, 1, Length[struktur])
darstellungwahrscheinlichkeiten = Zip(Text[W, P, false, true], W, wahrscheinlichkeiten, P, positionWahrscheinlichkeiten)
knotenbezeichner = Sequence(Element[Element[struktur, i], 5], i, 1, Length[struktur])
korrekturK: (-0.2, 0.3)
positionKnotenbezeichner = Sequence(Element[knotenmitten, i] + korrekturK, i, 1, Length[knotenmitten])
darstellungKnoten = Zip(Text[K, P, false, true], K, knotenbezeichner, P, positionKnotenbezeichner)
elemente = Sequence(If[Element[Element[tabelle, i], 1], Element[Element[tabelle, i], 2], ""], i, 1, Length[tabelle])
darstellungTabelleElemente = Zip(Text[E, P, false, true], E, elemente, P, positionenElemente)
wahrscheinlichkeitenTabelle = Sequence(If[Element[Element[tabelle, i], 1], Element[Element[tabelle, i], 3], ""], i, 1, Length[tabelle])
positionenWTabelle = Sequence(Element[positionenTabelle, i] + korrekturW, i, 1, Length[positionenTabelle])
darstellungTabelleWahrscheinlichkeiten = Zip(Text[E, P, false, true], E, wahrscheinlichkeitenTabelle, P, positionenWTabelle)
wBerechnet = Sequence(If[Element[Element[tabelle, i], 1], LaTeX[(anzahlWdh * Element[Element[tabelle, i], 4])], ""], i, 1, Length[tabelle])
Elemente = 1.2 (slider from -5 to 5, step 0.1)
posWTabelle = 1 (slider from -5 to 5, step 0.1)
posStufe1: (ah1 - r | hBaum + 0.5)
posStufe2: (ah1 + ah2 - r | hBaum + 0.5)
posStufe3: (ah1 + ah2 + ah3 - r | hBaum + 1)
tStufe1 = Text("1. Kugel", posStufe1)
tStufe2 = Text("2. Kugel", posStufe2)
stellungwahscheinlichkeiten = 1 (slider from -5 to 5, step 0.1)
arstellungErgebnisseElemente = 1 (slider from -5 to 5, step 0.1)
arstellungTabelleErgebnisse = 1 (slider from -5 to 5, step 0.1)
KopfErgebnisse = 1 (slider from -5 to 5, step 0.1)
KopfStufe1 = 1 (slider from -5 to 5, step 0.1)
KopfStufe2 = 1 (slider from -5 to 5, step 0.1)
KopfStufe3 = 1 (slider from -5 to 5, step 0.1)
Stufe = 1 (slider from -5 to 5, step 0.1)
m1: {{"O", (0 | 0 | 0), (0 | 0 | 0), "\frac16", "6", (1 | 0 | 0), (1 | 0 | 0)}, {"K", (1 | 0 | 0), (1 | 0 | 0), "\frac16", "6", (1 | 1 | 0), (1 | 1 | 0)}, {"K", (1 | 1 | 0), (1 | 1 | 0), "\frac16", "6", (1 | 1 | 1), (1 | 1 | 1)}, {"K", (1 | 1 | 0), (1 | 1 | 0), "\frac56", "\overline6", (1 | 1 | 1), (1 | 1 | -1)}, {"K", (1 | 0 | 0), (1 | 0 | 0), "\frac56", "\overline6", (1 | 1 | 0), (1 | -1 | 0)}, {"K", (1 | 1 | 0), (1 | -1 | 0), "\frac16", "6", (1 | 1 | 1), (1 | -1 | 1)}, {"K", (1 | 1 | 0), (1 | -1 | 0), "\frac56", "\overline6", (1 | 1 | 1), (1 | -1 | -1)}, {"O", (0 | 0 | 0), (0 | 0 | 0), "\frac56", "\overline6", (1 | 0 | 0), (-1 | 0 | 0)}, {"K", (1 | 0 | 0), (-1 | 0 | 0), "\frac16", "6", (1 | 1 | 0), (-1 | 1 | 0)}, {"K", (1 | 1 | 0), (-1 | 1 | 0), "\frac16", "6", (1 | 1 | 1), (-1 | 1 | 1)}, {"K", (1 | 1 | 0), (-1 | 1 | 0), "\frac56", "\overline6", (1 | 1 | 1), (-1 | 1 | -1)}, {"K", (1 | 0 | 0), (-1 | 0 | 0), "\frac56", "\overline6", (1 | 1 | 0), (-1 | -1 | 0)}, {"K", (1 | 1 | 0), (-1 | -1 | 0), "\frac16", "6", (1 | 1 | 1), (-1 | -1 | 1)}, {"K", (1 | 1 | 0), (-1 | -1 | 0), "\frac56", "\overline6", (1 | 1 | 1), (-1 | -1 | -1)}}
O: (0 | 0)
m2: {{"O", (0 | 0 | 0), (0 | 0 | 0), "\frac{1}{6}", "6", (1 | 0 | 0), (1 | 0 | 0), 1}, {"K", (1 | 0 | 0), (1 | 0 | 0), "\frac{1}{6}", "6", (1 | 1 | 0), (1 | 1 | 0), 2}, {"K", (1 | 1 | 0), (1 | 1 | 0), "\frac{1}{6}", "6", (1 | 1 | 1), (1 | 1 | 1), 3}, {"K", (1 | 1 | 0), (1 | 1 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 1), (1 | 1 | -1), 3}, {"K", (1 | 0 | 0), (1 | 0 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 0), (1 | -1 | 0), 2}, {"K", (1 | 1 | 0), (1 | -1 | 0), "\frac{1}{6}", "6", (1 | 1 | 1), (1 | -1 | 1), 3}, {"K", (1 | 1 | 0), (1 | -1 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 1), (1 | -1 | -1), 3}, {"O", (0 | 0 | 0), (0 | 0 | 0), "\frac{5}{6}", "\overline{6}", (1 | 0 | 0), (-1 | 0 | 0), 1}, {"K", (1 | 0 | 0), (-1 | 0 | 0), "\frac{1}{6}", "6", (1 | 1 | 0), (-1 | 1 | 0), 2}, {"K", (1 | 1 | 0), (-1 | 1 | 0), "\frac{1}{6}", "6", (1 | 1 | 1), (-1 | 1 | 1), 3}, {"K", (1 | 1 | 0), (-1 | 1 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 1), (-1 | 1 | -1), 3}, {"K", (1 | 0 | 0), (-1 | 0 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 0), (-1 | -1 | 0), 2}, {"K", (1 | 1 | 0), (-1 | -1 | 0), "\frac{1}{6}", "6", (1 | 1 | 1), (-1 | -1 | 1), 3}, {"K", (1 | 1 | 0), (-1 | -1 | 0), "\frac{5}{6}", "\overline{6}", (1 | 1 | 1), (-1 | -1 | -1), 3}}
eBw = Textfield(xBw)
eBf = Textfield(xBf)
R2w = 1 (slider from -5 to 5, step 0.1)
R2f = 1 (slider from -5 to 5, step 0.1)
d: (xBw * R2f)
tBf = Text("P(\overline{B}) = ", (0 | 0), true, true)
R1w = 1 (slider from -5 to 5, step 0.1)
tBw = Text("P(B) =", (0 | 0), true, true)
tBwAw = Text("P_{B}(A) = ", (0 | 0), true, true)
tBwAf = Text("P_{B}(\overline{A}) = ", (0 | 0), true, true)
tBfAw = Text("P_{\overline{B}}(A) = ", (0 | 0), true, true)
tBfAf = Text("P_{\overline{B}}(\overline{A}) = ", (0 | 0), true, true)
eBwAf = Textfield(xBwAf)
eBfAw = Textfield(xBfAw)
eBfAf = Textfield(xBfAf)
posR1f: Element[positionWahrscheinlichkeiten, 4] + korrekturPosE
posR1fR2f: Element[positionWahrscheinlichkeiten, 6] + korrekturPosE
posR1fR2w: Element[positionWahrscheinlichkeiten, 5] + korrekturPosE
posR1w: Element[positionWahrscheinlichkeiten, 1] + korrekturPosE
posR1wR2f: Element[positionWahrscheinlichkeiten, 3] + korrekturPosE
posR1wR2w: Element[positionWahrscheinlichkeiten, 2] + korrekturPosE
posEreignis: (ah1 + ah2 - r + 2, hBaum + 1)
xElemente: x(Element[positionenElemente, 1])
xWahrscheinlichkeiten: x(Element[positionenWTabelle, 1])
posKopfElemente: (xElemente, hBaum + 1)
tEreignis = Text("Ereignis", (0 | 0) + posKopfElemente)
posKopfWahrscheinlichkeiten: (xWahrscheinlichkeiten, hBaum + 1)
tWahrscheinlichkeit = Text("Wahrsch.", (0 | 0) + posKopfWahrscheinlichkeiten)
pAw: pBwAw + pBfAw
pAf: pBwAf + pBfAf
TextBw = Text("B", Element[positionKnotenbezeichner, 1], true, true)
TextBf = Text("\overline{B}", Element[positionKnotenbezeichner, 4], true, true)
TextBwAw = Text("A", Element[positionKnotenbezeichner, 2], true, true)
TextBwAf = Text("\overline{A}", Element[positionKnotenbezeichner, 3], true, true)
TextBfAw = Text("A", Element[positionKnotenbezeichner, 5], true, true)
TextBfAf = Text("\overline{A}", Element[positionKnotenbezeichner, 6], true, true)
eBwAw = Textfield(xBwAw)
a = 6 (slider from -5 to 10, step 0.1)
vTafel: a / 2
V1: (0 + vTafel | a / 2)
V2: (0 + vTafel | (-(a / 2)))
V3: (a + vTafel | (-(a / 2)))
V4: (a + vTafel | a / 2)
pBw: xBw
AfBw = 1 (slider from -5 to 5, step 0.1)
Bf = 1 (slider from -5 to 5, step 0.1)
V5: V2 + ((pBw * a) | 0)
V9: V1 + ((pBw * a) | 0)
V6: V5 + (0 | (xBwAf * a))
V7: V2 + (0 | (xBwAf * a))
V8: V5 + (0 | (xBfAf * a))
V10: V3 + (0 | (xBfAf * a))
vBwAw = Polygon({V1, V7, V6, V9})
vBfAw = Polygon({V9, V8, V10, V4})
vBwAf = Polygon({V7, V2, V5, V6})
vBfAf = Polygon({V8, V5, V3, V10})
sQ4 = Segment(V1, V2)
sQ1 = Segment(V4, V1)
sQ2 = Segment(V2, V3)
sQ3 = Segment(V7, V6)
sQ5 = Segment(V9, V5)
sQ6 = Segment(V3, V4)
sQ7 = Segment(V8, V10)
pBwIAw: pBwAw / pAw
pBwIAf: pBwAf / pAf
pBfIAw: pBfAw / pAw
pBf: xBf
pBfIAf: pBfAf / pAf
WBwAw = Element(positionenTabelle, 2)
WBwAf = Element(positionenTabelle, 3)
WBfAf = Element(positionenTabelle, 6)
WBfAw = Element(positionenTabelle, 5)
Text23: "\frac{P(A \cap B)}{P(A)} = " + (LaTeX[pBwIAw]) + ""
Text25: "\frac{P(A\cap \overline{B})}{P(A)} = " + (LaTeX[pBfIAw]) + ""
Text24: "\frac{P(\overline{A} \cap B)}{P(\overline{A})} = " + (LaTeX[pBwIAf]) + ""
Text26: "\frac{P(\overline{A} \cap \overline{B})}{P(\overline{A})} = " + (LaTeX[pBfIAf]) + ""
Text28: "P(\overline{A} \cap B) + P(\overline{A} \cap \overline{B}) = \\" + (LaTeX[pAf]) + ""
Text27: "P(A \cap B) + P(A \cap \overline{B}) = \\" + (LaTeX[pAw]) + ""
n = 1000 (slider from -5 to 2000000, step 0.1)
Eingabefeld1 = Textfield(n)
Pw = 1 (slider from -5 to 5, step 0.1)
HBw: (pBw * n)
HBf: (pBf * n)
HBwAw: (pBwAw * n)
HBwAf: (pBwAf * n)
HBfAw: (pBfAw * n)
HBfAf: (pBfAf * n)
g = true
h = false
Text42: "P(B) \cdot P_{B}(A) = \\" + (LaTeX[pBwAw]) + ""
Text43: "P(B) \cdot P_{B}(\overline{A}) = \\" + (LaTeX[pBwAf]) + ""
Text44: "P(\overline{B}) \cdot P_{\overline{B}}(A) = \\" + (LaTeX[pBfAw]) + ""
Text45: "P(\overline{B}) \cdot P_{\overline{B}}(\overline{A}) = \\" + (LaTeX[pBfAf]) + ""
Text46: "" + (LaTeX[HBwAw]) + ""
Text47: "" + (LaTeX[HBwAf]) + ""
Text48: "" + (LaTeX[HBfAw]) + ""
Text49: "" + (LaTeX[HBfAf]) + ""
Text51: "" + (LaTeX[HBf]) + ""
WBw = Element(positionenTabelle, 1)
WBf = Element(positionenTabelle, 4)
Text50: "" + (LaTeX[HBw]) + ""
Text56: "H(A \cap B) + H(A \cap \overline{B}) = \\" + (LaTeX[(pAw * n)]) + ""
Text57: "H(\overline{A} \cap B) + H(\overline{A} \cap \overline{B}) = \\" + (LaTeX[(pAf * n)]) + ""
Text61: "\frac{H(\overline{A} \cap B)}{H(\overline{A})} = " + (LaTeX[pBwIAf]) + ""
Text62: "\frac{H(A\cap \overline{B})}{H(A)} = " + (LaTeX[pBfIAw]) + ""
Text63: "\frac{H(\overline{A} \cap \overline{B})}{H(\overline{A})} = " + (LaTeX[pBfIAf]) + ""
Text55: "\frac{H(A \cap B)}{H(A)} = " + (LaTeX[pBwIAw]) + ""
i = false
Text64: "" + (LaTeX[xBf]) + ""
Text65: "" + (LaTeX[xBwAf]) + ""
Text66: "" + (LaTeX[xBfAw]) + ""
Text6: "P(\overline{A}|B) = " + (LaTeX[xBwAf]) + ""
Text5: "P(A|B) = " + (LaTeX[xBwAw]) + ""
Text17: "P(A|\overline{B}) = " + (LaTeX[xBwAf]) + ""
Text18: "P(\overline{A}|\overline{B}) = " + (LaTeX[xBfAf]) + ""