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Waffle Chart Visualization

This waffle chart demonstrates how conditional probability differs from total probability. While the total probability P(Event) considers all possible outcomes equally, conditional probability P(Event | Condition) restricts our view to specific regions. When you know which region you are in, the likelihood of the event changes dramatically.

Region A0.15
P(
| Region A)P(
|
)
Region B0.40
P(
| Region B)P(
|
)
Region C0.65
P(
| Region C)P(
|
)
Region D0.85
P(
| Region D)P(
|
)

Adjust Distribution

15/100
40/100
65/100
85/100
Understanding conditional probability: Each region has 100 tiles with equal probability P(Region) = 0.25. The
dark blue tiles represent the same event across all regions. P(
|
) = (dark tiles in that region) / 100. The total probability P(
) is calculated using the law of total probability: sum of P(Region) × P(
| Region) across all regions. Notice how conditional probabilities vary by region—knowing which region you are in changes the likelihood of the event.

Total: P(
)

Total probability:
0.512
205 of 400 tiles
Law of Total Probability:
P(
) · P(
|
)
+ P(
) · P(
|
)
+ P(
) · P(
|
)
+ P(
) · P(
|
)
= 0.25·0.15 + 0.25·0.40 + 0.25·0.65 + 0.25·0.85
= 0.512

Grid-Based Probability
Visualizing Conditions
Intuitive Understanding



Understanding Conditional Probability with Waffle Charts

Waffle charts use a grid of squares to represent probabilities as proportions. Each square represents an equal portion of the sample space. When applying conditions, relevant squares are highlighted, making it easy to see how probabilities change.



Grid-Based Probability

Waffle charts divide the sample space into equal squares, typically 100 or more. Each square has the same probability, making it easy to count and calculate proportions visually.
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Visualizing Conditions

When a condition is applied, the chart highlights only relevant squares. P(A|B) becomes a simple counting exercise: count squares that are both A and B, divide by squares that are B.
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Intuitive Understanding

Waffle charts are particularly effective for helping students understand proportions and percentages. They're widely used in data visualization for survey results, demographics, and risk assessment.
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