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Grade 10 · Conditional probability

Recycling records: Restrict a conditional sample space

Recycling records investigation: restrict a conditional sample space. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Recycling records: Restrict a conditional sample space. Chosen-group size: 7. All people/items: 10. Success within chosen group: 42.857%. Excluded from denominator: 3Conditioning changes the denominator3 / 742.857%Outside: 3Faded cases are outside the chosen group.
Selection is uniform among members of the chosen group, whose size is positive. Outcomes outside that group are deliberately unspecified and are not treated as failures. This is a count-based conditional model, not a causal claim.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Chosen-group size
7
All people/items
10
Success within chosen group
42.857%
Excluded from denominator
3

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From experiment to screen.

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Understand what you are seeing

The idea behind the motion.

Conditioning restricts the sample space to cases meeting a specified condition. The denominator becomes the size of that chosen group, rather than the size of the entire collection. Counts outside the group disappear from the conditional calculation even when they were visible initially. This investigation begins with successes in chosen group = 3; failures in chosen group = 4; cases outside chosen group = 3. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

P(success | chosen group) = successes / (successes + failures)

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Represent the given quantities

    Within the chosen group, count a successes and b failures. The other c cases do not satisfy the condition.

  2. STEP 2

    Follow the changing model

    Playback fades the outside-group cases, leaving the appropriate denominator visible.

  3. STEP 3

    Check and explain the relationship

    Divide a by a+b. Changing c should not change this conditional probability because those cases are excluded.

Your turn to explain

Make a prediction. Test your reasoning.

Recycling records: A chosen group has 3 successes and 4 failures; 3 cases are outside that group. Find P(success | chosen group).

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

3/7 = 42.857%. The 3 outside cases are excluded from the denominator.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 10 · Statistics

Change the denominator when a condition is given

Calculate a conditional relative frequency from a two-way count table.