Data & Probability · Probability · 3.3

Complement (P of not).

The complement of an event is everything that ISN’T that event. Since all probabilities total 1, P(not A) = 1 − P(A). If P(blue) = 2/6 = 1/3, then P(not blue) = 1 − 1/3 = 2/3.

01 / THE IDEA

See it work.

Watch the method

Complement (P of not)

P(not A) = 1 − P(A).

1 / 2
A spinner of 6 equal sections has 2 blue. P(not blue)?
1

Complement rule

P(not A) = 1 − P(A): every outcome that isn’t favorable.

1−261 - \frac{2}{6}
2

Subtract & simplify

The remaining outcomes over the total, reduced.

46=2/3\frac{4}{6} = 2/3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type the answer as a fraction, decimal, or percent (e.g. 1/4, 0.25, 25%).

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

The rest of the outcomes

The favorable and unfavorable probabilities add to 1.

Why it works

What’s left over.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A spinner of 5 equal sections has 4 blue. P(not blue)?

1

Complement rule

P(not A) = 1 − P(A): every outcome that isn’t favorable. 1 - 4/5

2

Subtract & simplify

The remaining outcomes over the total, reduced. 1/5 = 1/5

EX 2medium

A spinner of 10 equal sections has 1 blue. P(not blue)?

1

Complement rule

P(not A) = 1 − P(A): every outcome that isn’t favorable. 1 - 1/10

2

Subtract & simplify

The remaining outcomes over the total, reduced. 9/10 = 9/10

EX 3hard

A spinner of 5 equal sections has 2 blue. P(not blue)?

1

Complement rule

P(not A) = 1 − P(A): every outcome that isn’t favorable. 1 - 2/5

2

Subtract & simplify

The remaining outcomes over the total, reduced. 3/5 = 3/5

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to subtract from 1.

Fix

P(not A) = 1 − P(A), not just P(A).

Trap

Subtracting from the wrong whole.

Fix

The total of all probabilities is 1.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

A spinner of 6 equal sections has 2 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
C2

A spinner of 10 equal sections has 1 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
C3

A spinner of 6 equal sections has 3 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
C4

A spinner of 8 equal sections has 2 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
Apply

Apply (4)

A1

A spinner of 10 equal sections has 4 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
A2

A spinner of 8 equal sections has 3 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
A3

A spinner of 10 equal sections has 2 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
A4

A spinner of 6 equal sections has 2 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
Extension

Extension (4)

E1

A spinner of 10 equal sections has 9 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
E2

A spinner of 8 equal sections has 6 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
E3

A spinner of 8 equal sections has 5 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.
E4

A spinner of 10 equal sections has 8 blue. P(not blue)?

Need a hint?
  • Find P(A) first.
  • Subtract it from 1.