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.
Geben Sie 1-10000 Versuche ein (mehr Versuche = bessere Annäherung)
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
Theoretical probability is calculated using mathematical formulas. For a fair coin, the probability of heads is:
\(P(\text{Heads}) = \frac{1}{2} = 0.5\)Experimental probability is calculated from actual trial results:
\(P_{\text{experimental}} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}\)Law of Large Numbers
As the number of trials increases, the experimental probability approaches the theoretical probability. Therefore, more trials yield better approximations.
Dice Probability
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:
\(P(\text{sum} = 7 \text{ with 2 dice}) = \frac{6}{36} = \frac{1}{6}\)