Probability of an event and basic probability rules - One Line Questions

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