SME
Grade 10 Math · Problem type
Mutually exclusive events
Use this for “P(red) = 0.25 and P(blue) = 0.40 for one marble. Find P(red or blue).”
Diagram
P(Red) = 0.25
P(Blue) = 0.4
P(Red and Blue) = 0
Red only 0.25 − 0 = 0.25
Blue only 0.4 − 0 = 0.4
Red and Blue can't both happen (mutually exclusive), so P(Red or Blue) = P(Red) + P(Blue)
Shaded: P(Red ∪ Blue) = 0.25 + 0.4 = 0.65
This is an example. Type your own values to start a new problem.
P(Red
or
Blue)
=
P(Red)
+
P(Blue)
=
P(Red or Blue)
Formulas
P(Red or Blue) = P(Red) + P(Blue)
0.65 = 0.25 + 0.4
Assumptions
•
Mutually exclusive events share no outcome: P(A and B) = 0.
•
Their circles don’t overlap, so nothing is counted twice.
•
So P(A or B) = P(A) + P(B).
Step-by-step
WE KNOW
P(Red) = 0.25, P(Blue) = 0.4
FIND
P(Red or Blue) (P(Red or Blue))
Step 1 · Find P(Red or Blue): P(Red or Blue)
Use P(Red or Blue) = P(Red) + P(Blue)
Nothing is shared, so just add the two.
P(Red or Blue) = 0.25 + 0.4
P(Red or Blue) = 0.65
Check
Put the numbers back in. Both sides should match.
0.65 = 0.25 + 0.4 ✓
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