Independent Events

For independent events (like flipping a coin and rolling a die), the Multiplication Rule applies: .

Target: Make and

touch_app Drag axes to set probabilities

Area Model Calculation

{{ s1.valA.toFixed(1) }}
{{ s1.valB.toFixed(1) }}
{{ (s1.valA * s1.valB).toFixed(2) }}
check_circle Perfect! The intersecting area represents the compound probability.

Dependent Events

When drawing items without replacement, the probability changes!
Task: Find by dragging 2 Red candies to the plate.

Jar
Plate
Drag 1st Red Candy Here
Waiting for first draw...

1st Draw (Red):

Notice the jar has fewer candies now.
Drag another Red candy!

2nd Draw (Red):

Total Probability:

The Addition Rule

To find the probability of A OR B, we must subtract the intersection so it's not counted twice.
Drag the correct terms to build the formula for .

+
-

Checking Independence

Events are independent ONLY IF .
Build the test machine to find out if these events are independent.

Multiplication Check
{{ s4.slots[0].val }}
close
{{ s4.slots[1].val }}
{{ s4.calcProduct !== null ? s4.calcProduct.toFixed(2) : '---' }}
Actual Intersection
{{ s4.slots[2].val.toFixed(2) }}
{{ s4.slots[2] ? s4.slots[2].val.toFixed(2) : '---' }}
{{ s4.calcProduct.toFixed(2) === s4.slots[2].val.toFixed(2) ? '=' : '≠' }}
{{ chip.val }}

Master of Probability!

You've successfully navigated independent events, dependent draws, and the addition rule!