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

Red First, Then Blue

What are we looking for?

A specific sequence: red on the first draw AND blue on the second draw. Order matters! "Red then Blue" is different from "Blue then Red".

How does the first draw affect the second?

After drawing a red marble and keeping it out:

• Red marbles: 4 → 3 (one less)
• Blue marbles: 3 → 3 (unchanged)
• Total marbles: 7 → 6

This changes our probability for drawing blue!

Setup:

Bag: 4 red + 3 blue = 7 marbles total. Drawing without replacement.

Step-by-Step Solution

P(first marble is red)

4 red out of 7 total

P(second is blue | first was red)

After removing one red: 3 red, 3 blue remain (6 total). Blue marbles are still 3.

Multiply for the intersection

Result:

Interesting Observation

Notice that P(Red then Blue) = 2/7, which is the same as P(both Red)!

This is a coincidence of this specific bag composition. Both work out to 4/7 × 1/2 because after removing one red marble, there happen to be equal numbers of red and blue remaining.