JEE Main - Addition and multiplication theorems of probability Online Test (MCQ Quiz)

1. If A and B are two events, the probability of A or B occurring is given by:

A) P(A) + P(B) B) P(A) * P(B) C) P(A) + P(B) - P(A ∩ B) D) P(A) + P(B) + P(A ∩ B)

2. 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)

3. 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)

4. 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)

5. 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)

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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) = 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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

Addition and multiplication theorems of probability - Online Test

Test Results