Wiki-Quellcode von Lösung Fruchgummis
Version 14.1 von Stefan Martin am 2025/12/17 13:33
Zeige letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
| 1 | Die Wahrscheinlichkeit für das Ereignis E = "kein gelbes Fruchtgummi" lässt sich z. B. berechnen, in dem die Wahrscheinlichkeit des sog. Gegenereignisses ermittelt und diese schlussendlich von 1 subtrahiert wird: | ||
| 2 | |||
| 3 | {{formula}} | ||
| 4 | \begin{aligned} | ||
| 5 | P(E) & = 1-(P(\text{"gelb, gelb"}) + P(\text{"gelb, rot"}) + P(\text{"gelb, weiß"}) + P(\text{"gelb, grün"}) ) \\ | ||
| 6 | & = 1- (313⋅212+2⋅313⋅712+2⋅313⋅212+2⋅313⋅112) \\ | ||
| 7 | & = 1526 \\ | ||
| 8 | \end{aligned} | ||
| 9 | {{/formula}} | ||
| 10 | |||
| 11 | Die Aussage ist also richtig. | ||
| 12 | |||
| 13 | \begin{tikzpicture}[ | ||
| 14 | level distance=3.5cm, | ||
| 15 | level 1/.style={sibling distance=5cm}, | ||
| 16 | level 2/.style={sibling distance=1.6cm}, | ||
| 17 | edge from parent/.style={draw, -latex}, | ||
| 18 | every node/.style={font=\small} | ||
| 19 | ] | ||
| 20 | |||
| 21 | \node {} | ||
| 22 | child { node {Rot} | ||
| 23 | edge from parent node[left] {$\frac{7}{17}$} | ||
| 24 | child { node {Rot} edge from parent node[left] {$\frac{6}{16}$} } | ||
| 25 | child { node {Grün} edge from parent node[right] {$\frac{1}{16}$} } | ||
| 26 | child { node {Gelb} edge from parent node[right] {$\frac{3}{16}$} } | ||
| 27 | child { node {Weiß} edge from parent node[right] {$\frac{2}{16}$} } | ||
| 28 | } | ||
| 29 | child { node {Grün} | ||
| 30 | edge from parent node[left] {$\frac{1}{17}$} | ||
| 31 | child { node {Rot} edge from parent node[left] {$\frac{7}{16}$} } | ||
| 32 | child { node {Gelb} edge from parent node[right] {$\frac{3}{16}$} } | ||
| 33 | child { node {Weiß} edge from parent node[right] {$\frac{2}{16}$} } | ||
| 34 | } | ||
| 35 | child { node {Gelb} | ||
| 36 | edge from parent node[right] {$\frac{3}{17}$} | ||
| 37 | child { node {Rot} edge from parent node[left] {$\frac{7}{16}$} } | ||
| 38 | child { node {Grün} edge from parent node[right] {$\frac{1}{16}$} } | ||
| 39 | child { node {Weiß} edge from parent node[right] {$\frac{2}{16}$} } | ||
| 40 | } | ||
| 41 | child { node {Weiß} | ||
| 42 | edge from parent node[right] {$\frac{2}{17}$} | ||
| 43 | child { node {Rot} edge from parent node[left] {$\frac{7}{16}$} } | ||
| 44 | child { node {Grün} edge from parent node[right] {$\frac{1}{16}$} } | ||
| 45 | child { node {Gelb} edge from parent node[right] {$\frac{3}{16}$} } | ||
| 46 | }; | ||
| 47 | |||
| 48 | \end{tikzpicture} |