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Quiz Chapter 9: Probability of Combined Events

10 questions · Form 4 Mathematics Bab 9: Probability of Combined Events

Question 1 of 10Score: 0

If events A and B are mutually exclusive, what is P(A ∩ B)?

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. If events A and B are mutually exclusive, what is P(A ∩ B)?

  1. A. 1
  2. B. 0
  3. C. P(A) × P(B)
  4. D. P(A) + P(B)
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Answer: B

Mutually exclusive events cannot occur simultaneously, so their intersection P(A ∩ B) = 0.

2. A box contains 3 red balls and 7 blue balls. A ball is drawn at random and NOT replaced. A second ball is then drawn. What type of events are these?

  1. A. Mutually Exclusive Events
  2. B. Independent Events
  3. C. Dependent Events
  4. D. Complementary Events
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Answer: C

Because the first ball is not replaced, the composition of the box changes, affecting the probability of the second draw. Thus, they are dependent events.

3. Two fair coins are tossed. What is the probability of getting two heads or two tails?

  1. A. 14
  2. B. 12
  3. C. 34
  4. D. 1
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Answer: B

Sample space = {HH, HT, TH, TT}. Two heads = {HH}, Two tails = {TT}. They are mutually exclusive. P(HH or TT) = 14 + 14 = 24 = 12.

4. A box contains cards labeled with numbers 1 to 10. A card is drawn at random. Let A = prime numbers, B = multiples of 3. Find P(A ∪ B).

  1. A. 710
  2. B. 310
  3. C. 410
  4. D. 610
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Answer: A

A = {2, 3, 5, 7} → 4 items. B = {3, 6, 9} → 3 items. A ∩ B = {3} → 1 item. A ∪ B = {2, 3, 5, 6, 7, 9} → 6 items? Wait: Prime numbers in 1-10 are 2, 3, 5, 7 (4 items). Multiples of 3 are 3, 6, 9 (3 items). Union = {2, 3, 5, 6, 7, 9} which is 6 items. P(A ∪ B) = 610 or 35. Option D is 610.

5. A card is selected from a standard deck of 52 playing cards. Let A be getting a King and B be getting a Heart. Are events A and B mutually exclusive?

  1. A. Yes, because Kings and Hearts are different categories
  2. B. No, because the King of Hearts belongs to both events
  3. C. Yes, because P(A ∩ B) = 0
  4. D. Cannot be determined
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Answer: B

There is a card that is both a King and a Heart (King of Hearts), so P(A ∩ B) = 152 ≠ 0. They are not mutually exclusive.

6. A student takes two independent tests. Probability of passing Math is 0.8 and passing English is 0.9. Find the probability of passing Math but FAILING English.

  1. A. 0.72
  2. B. 0.08
  3. C. 0.18
  4. D. 0.02
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Answer: B

P(Pass Math) = 0.8. P(Fail English) = 1 - 0.9 = 0.1. P(Pass Math ∩ Fail English) = 0.8 × 0.1 = 0.08.

7. Which formula calculates the probability of union of two non-mutually exclusive events A and B?

  1. A. P(A ∪ B) = P(A) + P(B)
  2. B. P(A ∪ B) = P(A) × P(B)
  3. C. P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
  4. D. P(A ∪ B) = 1 - P(A ∩ B)
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Answer: C

For non-mutually exclusive events, overlapping outcomes counted twice must be subtracted: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

8. In a class of 30 students, 18 study Physics, 12 study Chemistry, and 5 study both. A student is picked at random. What is the probability that the student studies Physics OR Chemistry?

  1. A. 2530
  2. B. 3030
  3. C. 1830
  4. D. 2030
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Answer: A

P(P ∪ C) = P(P) + P(C) - P(P ∩ C) = 1830 + 1230 - 530 = 2530 = 56.

9. If P(A ∪ B) = 0.75, what is the probability of the complement event P((A ∪ B)')?

  1. A. 0.25
  2. B. 0.50
  3. C. 0.75
  4. D. 1.00
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Answer: A

P((A ∪ B)') = 1 - P(A ∪ B) = 1 - 0.75 = 0.25.

10. Using the same bag (5 red, 3 green), if two marbles are drawn WITHOUT replacement, what is the probability that both are red?

  1. A. 2564
  2. B. 514
  3. C. 2056
  4. D. 1028
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Answer: B

P(1st Red) = 58. P(2nd Red | 1st Red) = 47. P(Both Red) = (58) × (47) = 2056 = 514.

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