SME
Grade 10 Math · Geometry
Sample spaces, the addition rule, permutations and combinations
Use this for “P(band) = 0.45, P(sport) = 0.3 and P(both) = 0.12. Find P(band or sport).”
Diagram
P(Band) = 0.45
P(Sport) = 0.3
P(Band and Sport) = 0.12
Band only 0.45 − 0.12 = 0.33
Sport only 0.3 − 0.12 = 0.18
Shaded: P(Band ∪ Sport) = P(Band) + P(Sport) − P(Band ∩ Sport) = 0.45 + 0.3 − 0.12 = 0.63
This is an example. Type your own values to start a new problem.
P(Band
or
Sport)
=
P(Band)
+
P(Sport)
−
P(Band and Sport)
=
P(Band or Sport)
Formulas
P(Band or Sport) = P(Band) + P(Sport) − (P(Band and Sport))
0.63 = 0.45 + 0.3 − 0.12
Assumptions
•
P(A) and P(B) both count the overlap, so it is taken off once.
•
Each region shows its own probability; the whole rectangle is 1.
•
The shaded union is every outcome in A, in B or in both.
Step-by-step
WE KNOW
P(Band) = 0.45, P(Sport) = 0.3, P(Band and Sport) = 0.12
FIND
P(Band or Sport) (P(Band or Sport))
Step 1 · Find P(Band or Sport): P(Band or Sport)
Use P(Band or Sport) = P(Band) + P(Sport) − (P(Band and Sport))
Add the two, then take off the overlap counted twice.
P(Band or Sport) = 0.45 + 0.3 − 0.12
P(Band or Sport) = 0.63
Check
Put the numbers back in. Both sides should match.
0.63 = 0.45 + 0.3 − 0.12 ✓
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