Coin Flip & Dice Roll Simulator
Simulate coin flips and dice rolls to explore probability concepts. Track frequency distributions, compare experimental and theoretical probabilities, and visualize results with interactive charts.
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Theorie & Formel
What is probability simulation?
Probability simulation uses random number generation to model real random events. Through many trials, we can estimate theoretical probabilities by experimental results.
Theoretical vs. Experimental Probability
Die theoretische Wahrscheinlichkeit wird mit mathematischen Formeln berechnet. Bei einer fairen Münze beträgt die Wahrscheinlichkeit für Kopf:
\(P(\text{Heads}) = \frac{1}{2} = 0.5\)Experimental probability is calculated from actual trial results:
\(P_{\text{experimental}} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}\)Gesetz der großen Zahlen
As the number of trials increases, the experimental probability approaches the theoretical probability. Therefore, more trials yield better approximations.
Würfelwahrscheinlichkeit
For a single fair die, each number (1-6) has the same probability:
\(P(\text{rolling a 6}) = \frac{1}{6} \approx 0.167\)With multiple dice, some sums are more likely than others. For example, when rolling two dice:
\(P(\text{sum} = 7 \text{ with 2 dice}) = \frac{6}{36} = \frac{1}{6}\)