Practice Questions
Concept Explanation
The complement of event E is not E. Its probability is one minus the probability of E.
Key Formula
- P(not E) = 1 − P(E)
- P(at least one) often uses complement: 1 − P(none)
- Complements sum to 1: P(E) + P(not E) = 1
Example
Fair die: P(not 6) = 1 − 1/6 = 5/6.
Common Trap
Use complement when direct counting of at least one is lengthy.
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Q1 Easy
P(E) = 0.35. What is P(not E)?
ExplanationP(not E) = 1 − 0.35 = 0.65. -
Q2 Easy
Fair die rolled. What is P(not getting 6)?
ExplanationP = 1 − 1/6 = 5/6. -
Q3 Easy
P(rain) = 0.2. What is P(no rain)?
ExplanationP = 1 − 0.2 = 0.8. -
Q4 Medium
Two fair coins tossed. What is P(not both tails)?
Explanation1 − P(TT) = 1 − 1/4 = 3/4. -
Q5 Medium
One card drawn. What is P(not a king)?
ExplanationP = 1 − 4/52 = 48/52 = 12/13. -
Q6 Easy
Bag: 3 red, 7 blue. What is P(not blue)?
ExplanationP(red) = 3/10. -
Q7 Easy
P(E) = 3/8. What is P(not E)?
ExplanationP = 1 − 3/8 = 5/8.
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Q8 Medium
Three fair coins tossed. What is P(not all heads)?
Explanation1 − 1/8 = 7/8. -
Q9 Medium
Fair die rolled. What is P(not getting an even number)?
ExplanationOdd faces: P = 3/6 = 1/2. -
Q10 Medium
Two dice rolled. What is P(sum not equal to 7)?
Explanation1 − 6/36 = 30/36 = 5/6. -
Q11 Easy
P(E) = 0. What is P(not E)?
ExplanationImpossible event complement is certain: P = 1. -
Q12 Easy
One card drawn. What is P(not a red card)?
ExplanationP(black) = 26/52 = 1/2. -
Q13 Easy
P(E) = 1. What is P(not E)?
ExplanationCertain event complement is impossible: P = 0. -
Q14 Medium
Bag: 2 red, 8 blue. What is P(not red)?
ExplanationP(blue) = 8/10 = 4/5.
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DS1 Easy
What is P(not E)?
Statement IP(E) = 0.4.
Statement IIE and not E are complementary events.
ExplanationStatement I alone: P(not E) = 1 − 0.4 = 0.6. -
DS2 Easy
What is P(not getting 6 on a die roll)?
Statement IA fair die is rolled once.
Statement IIP(getting 6) = 1/6.
ExplanationNeed both: P = 1 − 1/6 = 5/6.
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DS3 Medium
What is P(not both tails when two coins are tossed)?
Statement ITwo fair coins are tossed.
Statement IIP(both tails) = 1/4.
ExplanationStatement II alone: P = 1 − 1/4 = 3/4. -
DS4 Medium
What is P(not a king when one card is drawn)?
Statement IA standard 52-card deck is used.
Statement IIP(king) = 1/13.
ExplanationNeed both: P = 1 − 1/13 = 12/13.