Loading...
Loading...
What does "mutually exclusive" mean?
Two events are mutually exclusive when they CANNOT happen at the same time. If one event happens, the other definitely did not happen.
Why are colors mutually exclusive?
A single marble can only be ONE color. If you draw a red marble, you did NOT draw a blue marble (even though the bag contains blue marbles). The same physical marble cannot be two colors.
The Big Simplification:
For mutually exclusive events, P(A AND B) = 0 (they can't both happen). So the inclusion-exclusion formula simplifies:
P(A OR B) = P(A) + P(B) - 0 = P(A) + P(B)
Simplified Formula (for mutually exclusive events):
A bag has 2 red, 3 blue, 4 green, and 1 yellow marble (10 total).
Example 1: P(Red OR Yellow)
Red and Yellow are mutually exclusive (can't be both). Just add:
Example 2: P(Blue OR Green)
Blue and Green are mutually exclusive. Just add:
Example 3: P(Red OR Blue OR Green)
This extends to multiple events! If they're all mutually exclusive (a marble can't be multiple colors), add them all:
Color categories are ALWAYS mutually exclusive for marbles — one marble = one color. Whenever you see "Color A OR Color B OR ...", you can simply add all the individual probabilities. No overlap means no subtraction needed!