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 EasyIn a campus quiz, P(E) = 0.35. What is P(not E)?ExplanationBy the complement rule, P(not E) = 1 − P(E) = 1 − 0.35 = 0.65. Hence the answer is 0.65.
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Q2 EasyA die is thrown. What is the probability of not getting a six?ExplanationP(getting 6) = 1/6. Using the complement: P(not 6) = 1 − 1/6 = 5/6. Hence the answer is 5/6.
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Q3 EasyIf P(rain) = 0.2, what is P(no rain)?ExplanationP(no rain) = 1 − 0.2 = 0.8. Hence the answer is 0.8.
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Q4 EasyP(E) = 3/8. What is P(not E)?ExplanationP(not E) = 1 − 3/8 = 5/8. Hence the answer is 5/8.
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Q5 EasyA bag has 3 red and 7 blue balls. One ball is drawn. What is P(not blue)?ExplanationNot blue means red: P = 3/10. Or 1 − 7/10 = 3/10. Hence the answer is 3/10.
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Q6 EasyIn an online test, one card is drawn. What is P(not a red card)?ExplanationP(red) = 1/2, so P(not red) = 1 − 1/2 = 1/2 (black cards). Hence the answer is 1/2.
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Q7 MediumTwo fair coins are tossed. What is the probability of not getting both heads?ExplanationOutcomes: HH, HT, TH, TT (each 1/4). P(both heads) = 1/4. P(not both heads) = 1 − 1/4 = 3/4. Hence the answer is 3/4.
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Q8 MediumOne card is drawn from a pack of 52 cards. What is the probability that it is not a face card?ExplanationFace cards = 12, so non-face = 40. P(not face) = 40/52 = 10/13. Or 1 − 12/52 = 40/52 = 10/13. Hence the answer is 10/13.
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Q9 MediumTwo fair dice are rolled. What is P(sum is not equal to 7)?ExplanationP(sum 7) = 6/36 = 1/6. P(sum ≠ 7) = 1 − 1/6 = 5/6. Hence the answer is 5/6.
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Q10 MediumThree fair coins are tossed. What is the probability of not getting three heads?ExplanationTotal outcomes = 8. P(HHH) = 1/8. P(not three heads) = 1 − 1/8 = 7/8. Hence the answer is 7/8.
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Q11 MediumA fair die is rolled. What is P(not getting an even number)?ExplanationEven faces: 2, 4, 6 so P(even) = 1/2. P(not even) = 1 − 1/2 = 1/2 (odd faces). Hence the answer is 1/2.
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Q12 MediumA bag has 2 red and 8 blue balls. One ball is drawn. What is P(not red)?ExplanationP(red) = 2/10 = 1/5. P(not red) = 1 − 1/5 = 4/5. Hence the answer is 4/5.
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Q13 MediumTwo fair coins are tossed. What is the probability of not getting both tails?ExplanationP(TT) = 1/4. P(not both tails) = 1 − 1/4 = 3/4. Hence the answer is 3/4.
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Q14 HardA and B are independent events with P(A) = 0.3 and P(B) = 0.4. What is P(neither A nor B)?ExplanationP(neither) = P(A′) × P(B′) for independent events = (1 − 0.3)(1 − 0.4) = 0.7 × 0.6 = 0.42. Hence the answer is 0.42.
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DS1 Easy
In a campus quiz, 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. Statement II alone is the definition and gives no numeric value. Answer: A. -
DS2 Easy
What is P(not getting 6 on a die roll)?
Statement IA fair six-sided die is rolled once.
Statement IIP(getting 6) = 1/6.
ExplanationI alone (fair die): P(not 6) = 5/6. II alone: P(not 6) = 1 − 1/6 = 5/6. Either alone is sufficient. Answer: D.
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DS3 Medium
What is P(not both heads when two coins are tossed)?
Statement ITwo fair coins are tossed.
Statement IIP(both heads) = 1/4.
ExplanationI alone: sample space of 4 outcomes ⇒ P(not HH) = 3/4. II alone: P = 1 − 1/4 = 3/4. Either alone is sufficient. Answer: D. -
DS4 Medium
What is P(not a face card when one card is drawn)?
Statement IA standard 52-card deck is used and one card is drawn.
Statement IIThere are 12 face cards in the deck.
ExplanationI alone lacks the face-card count. II alone lacks the total. Together: P = 1 − 12/52 = 40/52 = 10/13. Answer: C.