Conditional Probability Visual Lab

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关于这个模拟实验

KiwiBee’s rebuilt classroom probability lab uses a uniform sample space and two event intervals. Change P(A), P(B) and their feasible overlap, collect reproducible random trials, and switch between the full population and a population conditioned on A or B. Exact probabilities appear beside observed sample proportions. Changing a parameter starts a fresh experiment; conditioning on a zero-probability event is explicitly undefined. Inspired by Victor Powell’s MIT-licensed Explained Visually activity, with credits to Victor Powell and Lewis Lehe.

学生可以探索什么

Change the overlap and explain how the conditional denominator changes.
Add 100 trials and compare exact probabilities with sample proportions.
Set a conditioning event to zero and explain why its conditional proportion is undefined.

学习目标

1Explain conditional probability as a proportion within a restricted population.
2Distinguish P(B|A) from P(A|B).

教师常问的问题

Who created this activity and what is its source license?

Victor Powell; Explained Visually by Victor Powell and Lewis Lehe. Original source license: MIT. Source: https://github.com/vicapow/explained-visually. KiwiBee improves the classroom controls and experiments, retaining source credits and licenses.

What does this model simplify?

The falling balls are random samples from a simplified model. Short runs fluctuate, and a conditional probability is undefined when its conditioning event has probability zero.

How can I use the activity in class?

Use the activity controls inside the frame, or open fullscreen for a larger workspace. Ask students to predict a result, test it, and explain what changed. The embedded application starts in English; available upstream language controls are part of the original activity.

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继续探索

Spin a spinner, flip a coin or roll a die and watch two sets of bars: the chances the shapes predict, and the results you actually got. Ten spins prove nothing; a few hundred and the two are hard to tell apart.

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Type any function and see its shape straight away. Plot up to three at once in three colours to compare them, drag the trace point to read a value off a curve, and see where each one crosses zero.

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Move m and watch the line tilt; move b and watch it slide. Or drag the two points on the line and read the equation it writes back. A rise-over-run staircase climbs the line so slope becomes something you can count.

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Two-Body, Three-Body & N-Body Gravity的预览图

Compare a two-body orbit with three-body figure-eight motion, then add up to twelve bodies. Change initial masses, velocities and positions; watch orbit trails and numerical energy error.

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Riemann Sums and the Integral Simulation的预览图

Approximate the area under a curve with strips and choose how each takes its height: left edge, right edge, middle, or a sloping top. Push the strip count up and watch the error fall, with the running total plotted as its own curve.

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从模型到记录

学生探索之后，用工作表记录他们的预测、观察和解释。