SME
Grade 10 Math · Problem type
The complement rule
Use this for “The chance of rain is 0.35. What is the chance of no rain?”
Diagram
P(Rain) = 0.35
Rain and not Rain fill the rectangle: P(Rain) + P(not Rain) = 1
Shaded: P(not Rain) = 1 − P(Rain) = 1 − 0.35 = 0.65
This is an example. Type your own values to start a new problem.
P(not
Rain)
=
1
−
P(Rain)
=
P(not Rain)
Formulas
P(not Rain) = 1 − P(Rain)
0.65 = 1 − 0.35
Assumptions
•
Everything outside A is the complement of A, written A′ or “not A”.
•
A and not A together fill the rectangle, whose probability is 1.
•
So P(not A) = 1 − P(A).
Step-by-step
WE KNOW
P(Rain) = 0.35
FIND
P(not Rain) (P(not Rain))
Step 1 · Find P(not Rain): P(not Rain)
Use P(not Rain) = 1 − P(Rain)
Everything outside Rain: take P(Rain) from 1.
P(not Rain) = 1 − 0.35
P(not Rain) = 0.65
Check
Put the numbers back in. Both sides should match.
0.65 = 1 − 0.35 ✓
Topic check
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Sample spaces, the addition rule, permutations and combinations
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