This is the practice lab for the main probability lesson. The theory page now carries the chapter logic, while this page keeps the intuition-first explanations and animated dental simulations that make the ideas easier to feel.
Before you simulate, use these three ideas as your mental map. Then scroll into the dental examples and watch each concept update live with animation.
Probability runs from 0 to 1. As more implant outcomes are simulated, the observed success rate settles near the true value.
The expected value is a weighted average. In the DMFT example, it acts like the long-run center of the score distribution.
Variance describes spread. Two clinics can have similar averages but very different consistency, which matters for interpretation.
Probability is a number between 0 and 1 indicating how likely an event will occur. In dentistry, implant procedures, root canals, and fillings each carry specific success rates backed by clinical research.
Will this implant integrate successfully? Will a root canal relieve the patient's pain? These are questions of probability. By simulating many outcomes, we observe the Law of Large Numbers in action.
Try preset success rates, change the probability slider, and watch the observed rate move closer to the true value as more patients are simulated.
The expected value (mean) is the long-run average of outcomes, weighted by their probabilities. The DMFT index tracks Decayed, Missing, and Filled Teeth — a key measure in dental epidemiology.
Different populations show different DMFT distributions. A healthy group clusters near 0, while a high-risk group skews toward higher scores.
Open the simulator to choose a population, reshape the DMFT probabilities, and watch the running sample mean stabilize around the true expected value.
Drag the bars below to customize DMFT score probabilities, or select a preset. Then roll to see the sample mean converge to E[X].
Variance measures how spread out outcomes are from the expected value. In dentistry, patient satisfaction varies widely — some patients report excellent outcomes, others experience complications.
A low variance means consistent satisfaction; high variance signals unpredictable results. Understanding this spread is crucial for informed consent and treatment planning.
Launch the simulator to include or remove satisfaction scores, then draw repeated samples and compare the running variance with the true variance.
Toggle scores to include/exclude them from the population. Each score (1–10) represents a patient satisfaction rating. Draw samples and watch variance converge.