Practice MCQs – Probability

This MCQ set covers Probability as per NCERT Class 12 syllabus and CBSE board examination pattern.

1. P(A | B) is defined when:
   
   (A) P(A)=0
   
   (B) P(B)=0
   
   (C) P(B)≠0
   
   (D) A and B are independent
2. P(A | B) equals:
   
   (A) P(A)
   
   (B) P(B)
   
   (C) P(A ∩ B)/P(B)
   
   (D) P(B)/P(A)
3. If events A and B are independent, then:
   
   (A) P(A | B)=P(A)
   
   (B) P(A ∩ B)=0
   
   (C) P(A)=P(B)
   
   (D) A and B are mutually exclusive
4. Two mutually exclusive events are:
   
   (A) always independent
   
   (B) never independent
   
   (C) sometimes independent
   
   (D) always dependent
5. If P(A)=0.3 and P(B)=0.5, then P(A ∩ B) for independent events is:
   
   (A) 0.8
   
   (B) 0.15
   
   (C) 0.3
   
   (D) 0.5
6. P(A ∩ B) for independent events equals:
   
   (A) P(A)+P(B)
   
   (B) P(A)/P(B)
   
   (C) P(A)P(B)
   
   (D) P(A)−P(B)
7. Bayes’ theorem is used to find:
   
   (A) P(A ∩ B)
   
   (B) P(A)
   
   (C) P(A | B)
   
   (D) P(B)
8. Bayes’ theorem is based on:
   
   (A) addition theorem
   
   (B) multiplication theorem
   
   (C) conditional probability
   
   (D) permutations
9. Events A₁, A₂, …, Aₙ in Bayes’ theorem are:
   
   (A) dependent
   
   (B) mutually exclusive
   
   (C) independent
   
   (D) equally likely
10. Prior probabilities are:
    
    (A) after experiment
    
    (B) conditional probabilities
    
    (C) before experiment
    
    (D) posterior probabilities
11. Posterior probabilities are:
    
    (A) before experiment
    
    (B) after observing event
    
    (C) mutually exclusive
    
    (D) independent
12. If P(B)=0, then P(A | B) is:
    
    (A) 0
    
    (B) 1
    
    (C) undefined
    
    (D) equal to P(A)
13. A random variable is a function from:
    
    (A) R → S
    
    (B) S → R
    
    (C) R → R
    
    (D) S → S
14. Random variables are denoted by:
    
    (A) small letters
    
    (B) numbers
    
    (C) capital letters
    
    (D) symbols only
15. A discrete random variable has:
    
    (A) infinite values
    
    (B) interval values
    
    (C) countable values
    
    (D) continuous values
16. An example of discrete random variable is:
    
    (A) height
    
    (B) weight
    
    (C) number of heads
    
    (D) temperature
17. An example of continuous random variable is:
    
    (A) number of students
    
    (B) number of cars
    
    (C) height of a person
    
    (D) number of heads
18. Random variable may take:
    
    (A) only positive values
    
    (B) only integers
    
    (C) negative values also
    
    (D) only whole numbers
19. If X is a random variable, then X=x represents:
    
    (A) an event
    
    (B) an outcome
    
    (C) a number
    
    (D) sample space
20. Conditional probability reduces sample space to:
    
    (A) S
    
    (B) A
    
    (C) B
    
    (D) A ∩ B
21. If P(A|B)=P(A), then A and B are:
    
    (A) mutually exclusive
    
    (B) independent
    
    (C) dependent
    
    (D) exhaustive
22. Which is NOT required for Bayes’ theorem?
    
    (A) Mutually exclusive events
    
    (B) Exhaustive events
    
    (C) P(B)≠0
    
    (D) Independence of events
23. P(A ∩ B) ≤:
    
    (A) P(A)
    
    (B) P(B)
    
    (C) both A and B
    
    (D) P(A)+P(B)
24. The value of P(A | B) lies between:
    
    (A) −1 and 1
    
    (B) 0 and 1
    
    (C) 1 and 2
    
    (D) 0 and ∞
25. The sample space is:
    
    (A) event
    
    (B) outcome
    
    (C) set of all outcomes
    
    (D) probability
26. P(A ∪ B) equals:
    
    (A) P(A)+P(B)
    
    (B) P(A)+P(B)−P(A∩B)
    
    (C) P(A)P(B)
    
    (D) P(A|B)
27. If P(A)=1, then A is:
    
    (A) impossible
    
    (B) sure event
    
    (C) random event
    
    (D) empty set
28. If P(A)=0, then A is:
    
    (A) sure event
    
    (B) random event
    
    (C) impossible event
    
    (D) sample space
29. The complement of event A is denoted by:
    
    (A) A
    
    (B) A̅
    
    (C) A∩B
    
    (D) A∪B
30. P(A̅) equals:
    
    (A) 1−P(A)
    
    (B) P(A)
    
    (C) 1+P(A)
    
    (D) 0
31. The probability of sure event is:
    
    (A) 0
    
    (B) 1
    
    (C) −1
    
    (D) ∞
32. The probability of impossible event is:
    
    (A) 1
    
    (B) −1
    
    (C) 0
    
    (D) ∞
33. Bayes’ theorem helps in:
    
    (A) forward probability
    
    (B) backward probability
    
    (C) independent events
    
    (D) random variables
34. Which chapter follows random variables?
    
    (A) Bayes’ theorem
    
    (B) Probability distribution
    
    (C) Permutations
    
    (D) Statistics
35. Which is compulsory for conditional probability?
    
    (A) P(A)=0
    
    (B) P(B)=0
    
    (C) P(B)≠0
    
    (D) A and B independent
36. Independent events satisfy:
    
    (A) P(A|B)=P(A)
    
    (B) P(A|B)=0
    
    (C) P(A|B)=1
    
    (D) P(A|B)=P(B)
37. The sum of probabilities of all outcomes is:
    
    (A) 0
    
    (B) 1
    
    (C) 2
    
    (D) ∞
38. Which is NOT a random variable?
    
    (A) Number of heads
    
    (B) Height
    
    (C) Colour of car
    
    (D) Weight
39. Probability is defined on:
    
    (A) real numbers
    
    (B) integers
    
    (C) sample space
    
    (D) events
40. Conditional probability depends on:
    
    (A) event A only
    
    (B) event B only
    
    (C) occurrence of B
    
    (D) sample space only
41. Bayes’ theorem uses:
    
    (A) prior probabilities
    
    (B) posterior probabilities
    
    (C) both A and B
    
    (D) none
42. The value of probability cannot be:
    
    (A) 0
    
    (B) 1
    
    (C) −0.5
    
    (D) 0.8
43. Random variables are used to:
    
    (A) count outcomes
    
    (B) assign numbers to outcomes
    
    (C) form sample space
    
    (D) define events
44. Probability is a measure of:
    
    (A) certainty
    
    (B) randomness
    
    (C) likelihood
    
    (D) all of these
45. Which topic has highest weightage in Probability?
    
    (A) Conditional probability
    
    (B) Bayes’ theorem
    
    (C) Random variables
    
    (D) All of these