Intersection: Marbles

P(A ∩ B) with marble examples

Calculator Dice Coins Marbles Cards Learn

Two Red Marbles2 Red Red Then BlueR then B Specific SequenceSequence

Specific Sequence: Red, Blue, Red

What is a "specific sequence"?

We need exactly: Red on draw 1, Blue on draw 2, Red on draw 3. Any other order (like B-R-R or R-R-B) does NOT count.

What is the "Chain Rule"?

For a sequence of dependent events, we multiply conditional probabilities:

Each probability is calculated based on what happened before.

Setup:

Bag: 3 red + 2 blue = 5 marbles. Drawing 3 marbles without replacement.

Step-by-Step Solution

P(1st draw is Red)

Bag has: 3 red, 2 blue = 5 total

P(2nd draw is Blue | 1st was Red)

After removing one red: 2 red, 2 blue = 4 total

P(3rd draw is Red | 1st Red, 2nd Blue)

After R then B removed: 2 red, 1 blue = 3 total

Multiply all probabilities together

Result:

Tracking the Bag State

Time

Red

Blue

Total

Start

After R

After R,B

Key Insight: The Chain Rule Pattern

For any sequence of n events without replacement, keep a "running total" of what's left in the bag. Each probability uses the current state as its denominator and the count of the desired color as its numerator.