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12 Commits
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| b06b64739f | |||
| 47775e9941 | |||
| 0e5a22f062 | |||
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| 611c728f9e | |||
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| 1d60d4fb5c | |||
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| 8a6907e5c7 | |||
| 2b88234c14 |
@@ -137,7 +137,7 @@
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\begin{align*}
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\Omega &= \mleft\{(i,j): i,j \in \mleft\{
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1,\ldots, 6 \mright\}\mright\} \\
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A &= \mleft\{ (1,1),(2,2), \ldots, (6,6) \mright\}
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A &= \mleft\{ (1,1),(1,2), \ldots, (6,6) \mright\}
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\end{align*}
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\vspace*{-12mm}
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\end{lightgrayhighlightbox}
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@@ -275,17 +275,17 @@
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\item mindestens ein Ass hat?\pause
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\begin{gather*}
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P(\text{mindestens ein Ass}) = 1 - P(\text{kein Ass})
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= 1 - \frac{\binom{4}{0}\binom{48}{5}}{\binom{52}{5}} \approx 0,341
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= 1 - \frac{\binom{4}{0}\binom{48}{5}}{\binom{52}{5}} \approx 0{,}341
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\end{gather*}\pause\vspace*{-5mm}
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\item genau ein Ass hat?\pause
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\begin{gather*}
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P(\text{genau ein Ass}) = \frac{\binom{4}{1}\binom{48}{4}}{\binom{52}{5}} \approx 0,299
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P(\text{genau ein Ass}) = \frac{\binom{4}{1}\binom{48}{4}}{\binom{52}{5}} \approx 0{,}299
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\end{gather*}\pause
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\item mindestens zwei Karten der gleichen Art (“Paar”) hat?\pause
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\begin{align*}
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P(\text{mindestens zwei gleiche Karten}) &= 1 - P(\text{alle Karten unterschiedlich}) \\
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&= 1 - \frac{\text{Anzahl Möglichkeiten mit nur unterschiedlichen Karten}}{\text{Anzahl Möglichkeiten}}\\
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&= 1 - \frac{\binom{13}{5}\cdot 4^5}{\binom{52}{5}} \approx 0,493
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&= 1 - \frac{\binom{13}{5}\cdot 4^5}{\binom{52}{5}} \approx 0{,}493
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\end{align*}
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\end{enumerate}
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% tex-fmt: on
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@@ -372,7 +372,7 @@
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\begin{lightgrayhighlightbox}
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Beispiel:
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\begin{gather*}
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\Omega = {A, B, C}\\
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\Omega = \{A, B, C\}\\
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\Pi_N = \{ (A,B,C), (A,C,B), (B,A,C),\\
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(B,C,A), (C,A,B), (C,B,A)\}
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\end{gather*}
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