Visual Tools
Calculators
Tables
Mathematical Keyboard
Converters
Other Tools


Conditional Probability 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