Probability, Permutation and Combination, Statistics - Question Bank

1. The sum of 8 numbers is 320. If one number is removed, the mean of the remaining 7 numbers is 35. What is the removed number?
A) 35
B) 40
C) 50
D) 60
2. How many permutations are possible for the letters of the word 'ASSASSINATION'?
A) 13! / (4! * 3! * 2!)
B) 13! / (4! * 3! * 2! * 2!)
C) 13! / (4! * 3! * 3!)
D) 13!
3. A bag contains 4 red and 6 black balls. If two balls are drawn at random, what is the probability that one is red and the other is black?
A) 24/45
B) 12/45
C) 10/45
D) 1/45
4. The mean of the first 5 even numbers is:
A) 6
B) 8
C) 10
D) 12
5. In how many ways can 6 distinct items be arranged in a line?
A) 6
B) 36
C) 720
D) 120
6. A number is chosen at random from the numbers 1 to 30. What is the probability that the number is a multiple of 5?
A) 1/5
B) 6/30
C) 5/30
D) 1/6
7. The mean of 8 numbers is 40. If one number is removed, the mean of the remaining 7 numbers is 38. What is the removed number?
A) 38
B) 40
C) 50
D) 54
8. What is the value of ⁶C₄?
A) 6
B) 15
C) 30
D) 24
9. Two cards are drawn from a deck of 52 cards without replacement. What is the probability that both are hearts?
A) 1/17
B) 13/51
C) 13/52
D) 1/16
10. The mode of the data set: 10, 12, 15, 12, 10, 12, 15, 12 is:
A) 10
B) 12
C) 15
D) Cannot be determined
11. In how many ways can a president, vice-president, and secretary be chosen from a group of 10 people?
A) 100
B) 720
C) 120
D) 10!
12. A die is rolled once. What is the probability of getting a number greater than 4?
A) 1/6
B) 2/6
C) 3/6
D) 4/6
13. The median of the data set: 5, 2, 8, 1, 9, 4, 7 is:
A) 4
B) 5
C) 6
D) 7
14. What is the value of ⁹P₃?
A) 84
B) 27
C) 504
D) 729
15. From a group of 7 men and 6 women, a committee of 5 people is to be formed. What is the probability that the committee has exactly 3 men?
A) 210/429
B) 126/429
C) 105/429
D) 21/429
16. The mean of the first 6 positive integers is:
A) 3
B) 3.5
C) 4
D) 4.5
17. How many ways can 4 different colors be arranged in a circle?
A) 4
B) 12
C) 24
D) 6
18. A coin is tossed. What is the probability of getting a head?
A) 0
B) 1/2
C) 1
D) Cannot be determined
19. The sum of 5 numbers is 100. Their mean is 20. If one number is removed, the sum of the remaining 4 numbers is 80. What is the removed number?
A) 10
B) 15
C) 20
D) 25
20. In how many ways can the letters of the word 'ENGINEERING' be arranged?
A) 11! / (3! * 3! * 2!)
B) 11! / (3! * 2! * 2!)
C) 11! / (3! * 3! * 2! * 2!)
D) 11!
21. A lottery has 10 prizes and 500 tickets. If you buy one ticket, what is the probability of winning a prize?
A) 1/10
B) 1/50
C) 1/500
D) 10/500
22. The mean of 10 numbers is 30. If each number is increased by 5, the new mean is:
A) 30
B) 35
C) 40
D) 50
23. What is the value of ⁸C₅?
A) 8
B) 56
C) 64
D) 336
24. If the probability of an event is 0.75, what is the probability of the event not occurring?
A) 0.25
B) 0.50
C) 0.75
D) 1.75
25. The median of the following data: 10, 12, 14, 16, 18, 20 is:
A) 14
B) 15
C) 16
D) 17
26. In how many ways can 4 boys and 3 girls be seated in a row so that all the girls sit together?
A) 720
B) 144
C) 5040
D) 24
27. A bag contains 3 red, 5 green, and 4 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A) 3/12
B) 5/12
C) 7/12
D) 9/12
28. The mean of the first 5 odd numbers is:
A) 5
B) 7
C) 9
D) 11
29. How many different arrangements can be made from the letters of the word 'BANANA'?
A) 720
B) 120
C) 60
D) 30
30. What is the probability of drawing a spade or an ace from a standard deck of 52 cards?
A) 4/13
B) 1/13
C) 17/52
D) 18/52
31. The average of 5 numbers is 27. If 45 is added to the numbers, the new average is:
A) 30
B) 32
C) 36
D) 40
32. In how many ways can 5 people be seated in a row?
A) 5
B) 25
C) 120
D) 60
33. A number is selected at random from the first 20 natural numbers. What is the probability that the number is a multiple of 3?
A) 3/20
B) 6/20
C) 7/20
D) 1/3
34. The mean of a set of 15 numbers is 25. If one number is removed, the mean of the remaining numbers is 23. What is the removed number?
A) 25
B) 53
C) 58
D) 63
35. What is the value of ⁵C₃?
A) 5
B) 10
C) 15
D) 20
36. A committee of 3 members is to be selected from 4 men and 5 women. What is the probability that the committee consists of 2 men and 1 woman?
A) 10/21
B) 12/21
C) 6/21
D) 1/21
37. Find the range of the following data: 15, 8, 22, 10, 18.
A) 8
B) 10
C) 14
D) 22
38. How many ways can the letters of the word 'SUCCESS' be arranged?
A) 5040
B) 420
C) 720
D) 840
39. A bag contains 6 green balls and 4 yellow balls. If one ball is drawn at random, what is the probability it is green?
A) 1/10
B) 4/10
C) 6/10
D) 1
40. If the mean of 5 numbers is 10, and the mean of 3 of these numbers is 8, what is the mean of the remaining 2 numbers?
A) 10
B) 12
C) 14
D) 15
41. What is the value of ⁶P₂?
A) 30
B) 60
C) 15
D) 720
42. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a King or a Queen?
A) 1/13
B) 2/13
C) 4/13
D) 8/52
43. The mode of the data set: 2, 3, 4, 3, 5, 3, 2, 3 is:
A) 2
B) 3
C) 4
D) 5
44. In how many ways can 5 distinct books be arranged on a shelf?
A) 5
B) 25
C) 120
D) 60
45. Two dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 7?
A) 1/6
B) 5/36
C) 7/36
D) 1/12
46. Find the median of the following data set: 3, 7, 2, 8, 5, 9, 4.
A) 5
B) 6
C) 4
D) 7
47. How many permutations are there of the letters in the word 'APPLE'?
A) 120
B) 60
C) 24
D) 5
48. A coin is tossed three times. What is the probability of getting exactly two heads?
A) 1/8
B) 3/8
C) 1/2
D) 3/4
49. The mean of the first 10 natural numbers is:
A) 5
B) 5.5
C) 6
D) 10
50. In how many ways can a committee of 4 members be selected from a group of 10 people?
A) 210
B) 100
C) 5040
D) 24
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