Addition and multiplication theorems of probability - Question Bank

1. If P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.1, find P(A ∪ B).
A) 0.8
B) 0.9
C) 0.7
D) 0.6
2. Given P(A) = 0.7, P(B) = 0.5, and A and B are independent, find P(A ∪ B).
A) 0.85
B) 0.35
C) 1.2
D) 0.15
3. What is the probability of selecting a prime number or an even number from the integers 1 to 10?
A) 4/10
B) 5/10
C) 7/10
D) 6/10
4. If P(A) = 0.5, P(B) = 0.5, and A and B are mutually exclusive, what is P(A ∪ B)?
A) 0
B) 0.5
C) 1.0
D) 0.25
5. A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that the first is red and the second is blue?
A) 12/100
B) 24/100
C) 6/25
D) 12/25
6. Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.7, what is P(A ∩ B)?
A) 0.28
B) 0.3
C) 1.1
D) 0.7
7. If P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3, find P(A ∪ B).
A) 0.8
B) 1.0
C) 0.7
D) 0.9
8. What is the probability of drawing a red card or a face card from a standard deck of 52 cards?
A) 26/52
B) 12/52
C) 32/52
D) 38/52
9. If P(A) = 0.7, P(B) = 0.2, and A and B are mutually exclusive, what is P(A ∪ B)?
A) 0.9
B) 0.14
C) 0.5
D) 1.0
10. A number is selected at random from the first 10 positive integers. What is the probability that the number is even or a multiple of 3?
A) 7/10
B) 6/10
C) 8/10
D) 5/10
11. Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, what is P(A ∪ B)?
A) 0.65
B) 0.8
C) 0.15
D) 0.35
12. If P(A) = 0.5 and P(B) = 0.4, and P(A ∩ B) = 0.2, find P(A ∪ B).
A) 0.7
B) 0.9
C) 0.6
D) 0.8
13. Three fair coins are tossed. What is the probability of getting exactly two heads?
A) 1/8
B) 3/8
C) 1/2
D) 5/8
14. If P(A) = 0.8, P(B) = 0.7, and P(A ∩ B) = 0.6, find P(A ∪ B).
A) 0.9
B) 1.0
C) 0.8
D) 0.7
15. A card is drawn from a standard deck. What is the probability that it is a spade or a face card?
A) 13/52
B) 12/52
C) 25/52
D) 16/52
16. If P(A) = 1/2, P(B) = 1/4, and A and B are independent, what is P(A ∪ B)?
A) 1/8
B) 3/4
C) 5/8
D) 1/2
17. Two dice are rolled. What is the probability of getting a sum greater than 10?
A) 1/12
B) 1/9
C) 1/6
D) 5/36
18. If P(A) = 0.6, P(B) = 0.7, and P(A ∪ B) = 0.9, find P(A ∩ B).
A) 0.4
B) 0.3
C) 0.2
D) 0.5
19. What is the probability that a randomly chosen integer from 1 to 100 is divisible by 2 or 3?
A) 50/100
B) 33/100
C) 67/100
D) 17/100
20. If P(A) = 0.4, P(B) = 0.5, and P(A ∪ B) = 0.7, find P(A ∩ B).
A) 0.1
B) 0.2
C) 0.3
D) 0.4
21. A fair coin is tossed. What is the probability of getting a head or a tail?
A) 0
B) 0.5
C) 1
D) Cannot be determined
22. Two independent events A and B have P(A) = 0.5 and P(B) = 0.6. What is P(A ∪ B)?
A) 0.8
B) 0.9
C) 0.3
D) 1.1
23. If P(A) = 0.6 and P(A ∩ B) = 0.3, find P(B | A).
A) 0.5
B) 0.2
C) 1.0
D) 0.3
24. What is the probability of getting an odd number or a multiple of 3 when a single die is rolled?
A) 1/2
B) 2/3
C) 5/6
D) 1/3
25. If P(A) = 1/3, P(B) = 1/2, and A and B are mutually exclusive, what is P(A ∪ B)?
A) 1/6
B) 5/6
C) 1
D) 1/2
26. A letter is chosen at random from the word 'PROBABILITY'. What is the probability that the letter is 'B'?
A) 1/11
B) 2/11
C) 1/10
D) 3/11
27. If P(A) = 0.9 and P(B) = 0.8, and P(A ∩ B) = 0.75, find P(A ∪ B).
A) 0.95
B) 1.0
C) 0.85
D) 0.75
28. Two cards are drawn from a standard deck of 52 cards. What is the probability that both are hearts?
A) 1/13
B) 1/17
C) 1/221
D) 1/169
29. Let A and B be events such that P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.1. Find P(A ∪ B).
A) 0.7
B) 0.9
C) 0.6
D) 0.8
30. What is the probability of getting a sum of 5 when two dice are rolled?
A) 1/12
B) 1/9
C) 5/36
D) 1/6
31. If P(A) = 2/3, P(B) = 3/4, and A and B are independent, what is P(A ∩ B)?
A) 1/2
B) 5/12
C) 11/12
D) 3/4
32. A bag contains 5 red balls and 3 blue balls. If two balls are drawn without replacement, what is the probability that both are red?
A) 25/64
B) 15/28
C) 5/14
D) 10/21
33. If P(A) = 0.7, P(B) = 0.8, and P(A ∩ B) = 0.6, find P(A ∪ B).
A) 0.9
B) 1.0
C) 0.8
D) 0.7
34. What is the probability that a randomly selected leap year is divisible by 400?
A) 1/4
B) 1/100
C) 1/400
D) 1/5
35. Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)?
A) 0.1
B) 0.7
C) 1.0
D) 0.12
36. If P(A) = 0.6, P(B) = 0.4, and P(A ∩ B) = 0.2, find P(A ∪ B).
A) 0.8
B) 1.0
C) 0.7
D) 0.9
37. A coin is tossed three times. What is the probability of getting at least one head?
A) 1/8
B) 3/8
C) 7/8
D) 1/2
38. In a class of 30 students, 15 like Math, 10 like Science, and 5 like both. How many students like Math or Science?
A) 20
B) 25
C) 30
D) 15
39. If P(A) = 0.5 and P(B) = 0.5, and A and B are independent, what is P(A ∪ B)?
A) 0.5
B) 0.75
C) 1.0
D) 0.25
40. Two dice are rolled. What is the probability of getting a sum of 7?
A) 1/6
B) 5/36
C) 7/36
D) 1/4
41. What is the probability of drawing an ace or a king from a standard deck of 52 cards in a single draw?
A) 1/13
B) 2/13
C) 1/26
D) 1/52
42. Consider two events A and B. If P(A) = 1/2, P(B) = 1/3, and P(A ∩ B) = 1/6, find P(A ∪ B).
A) 1/2
B) 2/3
C) 5/6
D) 1
43. If P(A) = 0.3, P(B) = 0.5, and P(A ∪ B) = 0.7, what is P(A ∩ B)?
A) 0.1
B) 0.2
C) 0.3
D) 0.5
44. Given P(A) = 0.4, P(B) = 0.6, and A and B are independent events, what is P(A ∩ B)?
A) 0.24
B) 1.0
C) 0.1
D) 0.5
45. If P(A) = 0.5, P(B) = 0.7, and P(A ∩ B) = 0.3, what is P(A ∪ B)?
A) 0.9
B) 1.0
C) 0.8
D) 1.2
46. For any two events A and B, the probability of both A and B occurring is given by:
A) P(A ∪ B) = P(A) + P(B)
B) P(A ∩ B) = P(A) * P(B | A)
C) P(A ∩ B) = P(A) + P(B)
D) P(A ∩ B) = P(A) / P(B)
47. The multiplication theorem of probability for two independent events A and B states that the probability of both A and B occurring is:
A) P(A) + P(B)
B) P(A) * P(B)
C) P(A | B) * P(B)
D) P(B | A) * P(A)
48. If two events A and B are mutually exclusive, then P(A ∩ B) is:
A) P(A) * P(B)
B) 1
C) 0
D) P(A) + P(B)
49. For mutually exclusive events A and B, the probability of A or B occurring is:
A) P(A) + P(B) - P(A ∩ B)
B) P(A) * P(B)
C) P(A) + P(B)
D) 1 - P(A) - P(B)
50. The addition theorem of probability states that for any two events A and B:
A) P(A ∪ B) = P(A) + P(B)
B) P(A ∪ B) = P(A) + P(B) + P(A ∩ B)
C) P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
D) P(A ∩ B) = P(A) * P(B)
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