Union: Marbles

P(A ∪ B) with marble examples

Calculator Dice Coins Marbles Cards Learn

Red OR BlueR or B Overlapping EventsOverlap Mutually ExclusiveExclusive

Understanding "Red OR Blue"

What does "Red OR Blue" mean?

We want the probability of drawing a marble that is red OR blue. The marble could be red, or it could be blue — either one satisfies our condition.

Can a marble be BOTH red AND blue?

No! Each marble is exactly one color. A marble cannot be red and blue at the same time. This means red and blue are mutually exclusive events.

Why does this simplify things?

Since P(Red AND Blue) = 0, the union formula simplifies:

P(Red OR Blue) = P(Red) + P(Blue) - 0 = P(Red) + P(Blue)

Example: Red OR Blue Marble

Question

A bag has 3 red, 4 blue, and 3 green marbles (10 total). Draw one marble. What is P(Red OR Blue)?

The Setup:

red: 3

blue: 4

green: 3

Total: 10 marbles

Find P(Red)

3 red marbles out of 10 total:

Find P(Blue)

4 blue marbles out of 10 total:

Add them (mutually exclusive, no subtraction needed)

Result:

✓ Verification: 7 marbles (3 red + 4 blue) out of 10 = 70% ✓

Key Insight

When drawing from colored marbles, different colors are ALWAYS mutually exclusive. A marble has exactly one color. So for "Color A OR Color B" problems, just add the probabilities!