Probability of an event and basic probability rules - Question Bank

1. If the probability of an event is 0.8, the probability of its complement is:
A) 0.2
B) 0.8
C) 1.8
D) 0
2. What is the probability of getting a sum greater than 9 when rolling two fair dice?
A) 1/12
B) 5/36
C) 10/36
D) 1/6
3. The sum of probabilities of all elementary events in a sample space is:
A) Less than 1
B) Equal to 1
C) Greater than 1
D) Zero
4. Which rule is used to calculate the probability of the union of two events?
A) Addition Rule
B) Multiplication Rule
C) Complement Rule
D) Conditional Probability Rule
5. If P(A) = 1/2, P(B) = 1/3, and P(A ∪ B) = 3/4, find P(A ∩ B).
A) 1/12
B) 5/12
C) 7/12
D) 1/4
6. What is the probability that a number selected at random from {1, 2, 3, ..., 100} is divisible by 7?
A) 14/100
B) 15/100
C) 7/100
D) 1/7
7. A number is selected at random from the first 20 natural numbers. What is the probability that the number is divisible by 3 or 5?
A) 6/20
B) 4/20
C) 9/20
D) 7/20
8. If A and B are independent events, then P(A' and B') is equal to:
A) P(A') * P(B')
B) 1 - P(A or B)
C) P(A') + P(B')
D) P(A) * P(B)
9. If A and B are independent events, then P(A|B) is equal to:
A) P(A and B)
B) P(A) + P(B)
C) P(A)
D) P(B)
10. If P(A) = 0.4 and P(B) = 0.3, and A and B are independent events, what is P(A and B)?
A) 0.7
B) 0.1
C) 0.12
D) 0.4
11. In a standard deck of 52 cards, what is the probability of drawing a card that is neither a heart nor a king?
A) 39/52
B) 36/52
C) 35/52
D) 13/52
12. A single digit number is chosen at random from the digits 0 to 9. What is the probability that the chosen number is prime?
A) 3/10
B) 4/10
C) 7/10
D) 1/10
13. What is the probability of getting no heads when three fair coins are tossed?
A) 1/8
B) 3/8
C) 7/8
D) 1/2
14. Three fair coins are tossed. What is the probability of getting at least one head?
A) 1/8
B) 3/8
C) 7/8
D) 1/2
15. From the same bag (4 red, 6 blue, 5 green), what is the probability of drawing a ball that is NOT green?
A) 5/15
B) 10/15
C) 1/3
D) 2/3
16. A bag contains 4 red, 6 blue, and 5 green balls. What is the probability of drawing a blue ball?
A) 6/15
B) 4/15
C) 5/15
D) 1/2
17. If an event has probability 1, it means:
A) It is guaranteed not to occur.
B) It is equally likely to occur or not occur.
C) It is guaranteed to occur.
D) It will occur less than half the time.
18. If an event has 0 probability, it means:
A) It will occur exactly once.
B) It is guaranteed not to occur.
C) It is equally likely to occur or not occur.
D) It will occur half the time.
19. The odds against an event A are 2:5. What is the probability of event A?
A) 5/7
B) 2/7
C) 2/5
D) 5/2
20. The odds in favor of an event A are 3:2. What is the probability of event A?
A) 2/5
B) 3/5
C) 3/2
D) 2/3
21. If A and B are two events such that P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.1, find P(A ∪ B).
A) 0.9
B) 0.7
C) 0.8
D) 0.6
22. Let E be an event. Which statement is always true?
A) P(E) >= 0
B) P(E) <= 1
C) P(E) = 0 if E is impossible
D) All of the above
23. What is the probability that a randomly selected year is a leap year? (Assume 400 years cycle, with 97 leap years)
A) 1/4
B) 97/400
C) 100/400
D) 1/5
24. If P(A) = 0.25 and P(A') = 0.75, what can be concluded?
A) A is a sure event.
B) A is an impossible event.
C) The values are consistent with probability rules.
D) The values are inconsistent with probability rules.
25. In the previous scenario (10 red, 5 blue), what is the probability of drawing a blue ball?
A) 10/15
B) 5/15
C) 1/2
D) 15/10
26. If there are 10 red balls and 5 blue balls in a bag, what is the probability of drawing a red ball?
A) 10/15
B) 5/15
C) 10/5
D) 1/2
27. What is the probability of drawing a face card (Jack, Queen, King) from a standard deck of 52 cards?
A) 3/13
B) 12/52
C) 1/4
D) All of the above
28. In the experiment of rolling two fair dice, what is the probability of getting a sum of 7?
A) 1/36
B) 6/36
C) 7/36
D) 1/6
29. Consider the experiment of rolling two fair dice. What is the total number of possible outcomes?
A) 6
B) 12
C) 36
D) 2
30. Which of the following is NOT a basic rule of probability?
A) The probability of any event is between 0 and 1, inclusive.
B) The probability of the sample space is 1.
C) For mutually exclusive events A and B, P(A or B) = P(A) + P(B).
D) The probability of the complement of an event is 1 minus the probability of the event.
31. What does it mean if P(A) = 0?
A) Event A is certain to occur.
B) Event A is impossible.
C) Event A has a 50% chance of occurring.
D) Event A may or may not occur.
32. What does it mean if P(A) = 1?
A) Event A is impossible.
B) Event A is certain to occur.
C) Event A may or may not occur.
D) Event A has a 50% chance of occurring.
33. In a random experiment, the total number of possible outcomes is 25. If event E has 5 favorable outcomes, what is P(E)?
A) 1/25
B) 5/25
C) 1/5
D) 20/25
34. If P(A) = 0.7, what is P(not A)?
A) 0.3
B) 0.7
C) 1
D) 0
35. If P(A) = 0.6 and P(B) = 0.5, and P(A and B) = 0.2, what is P(A or B)?
A) 0.3
B) 0.7
C) 0.9
D) 1.1
36. If P(A) = 0.3 and P(B) = 0.4, and A and B are mutually exclusive events, what is P(A or B)?
A) 0.1
B) 0.7
C) 0.12
D) 0.3
37. What is the probability of drawing a spade from a standard deck of 52 playing cards?
A) 1/4
B) 1/13
C) 1/52
D) 1/2
38. A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a King?
A) 1/13
B) 4/13
C) 1/52
D) 1/4
39. Two fair coins are tossed. What is the probability of getting exactly one head?
A) 1/4
B) 1/2
C) 3/4
D) 1
40. What is the probability of getting an even number in a single throw of a fair die?
A) 1/3
B) 1/2
C) 2/3
D) 5/6
41. In a single throw of a fair die, what is the probability of getting a '4'?
A) 1/6
B) 2/6
C) 1/2
D) 5/6
42. What is the probability of the complement of an event A, denoted as P(A') or P(not A)?
A) 1 - P(A)
B) P(A)
C) 1 + P(A)
D) 0
43. For any two events A and B, which formula represents the probability of A or B?
A) P(A or B) = P(A) + P(B)
B) P(A or B) = P(A) * P(B)
C) P(A or B) = P(A) + P(B) - P(A and B)
D) P(A or B) = P(A) + P(B) + P(A and B)
44. If A and B are two mutually exclusive events, what is P(A and B)?
A) P(A) + P(B)
B) P(A) * P(B)
C) 0
D) 1
45. Let S be the sample space of an experiment. What is P(S)?
A) 0
B) 1
C) 0.5
D) Depends on the experiment
46. What is the probability of a sure event (an event that is certain to happen)?
A) 0
B) 0.5
C) 1
D) Any value between 0 and 1
47. What is the probability of an impossible event?
A) 1
B) 0.5
C) 0
D) Undetermined
48. Which of the following is a fundamental property of probability?
A) P(A) < 0
B) P(A) > 1
C) 0 <= P(A) <= 1
D) P(A) = -1
49. If an experiment has 'n' equally likely outcomes and event A has 'm' of these outcomes, what is the probability of event A?
A) n/m
B) m*n
C) m/n
D) n-m
50. What is the fundamental definition of probability of an event A, denoted as P(A)?
A) The number of outcomes not favorable to A divided by the total number of outcomes.
B) The ratio of the number of outcomes favorable to A to the total number of possible outcomes.
C) The sum of all possible outcomes.
D) The difference between favorable and unfavorable outcomes.
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