Probability, Permutation and Combination, Statistics - One Line Questions

1. A coin is tossed. What is the probability of getting a head? — 1/2
2. If the probability of an event is 0.75, what is the probability of the event not occurring? — 0.25
3. A bag contains 6 green balls and 4 yellow balls. If one ball is drawn at random, what is the probability it is green? — 6/10
4. A lottery has 10 prizes and 500 tickets. If you buy one ticket, what is the probability of winning a prize? — 1/50
5. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a King or a Queen? — 2/13
6. Two cards are drawn from a deck of 52 cards without replacement. What is the probability that both are hearts? — 1/17
7. A number is chosen at random from the numbers 1 to 30. What is the probability that the number is a multiple of 5? — 6/30
8. Two dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 7? — 1/6
9. A die is rolled once. What is the probability of getting a number greater than 4? — 3/6
10. A coin is tossed three times. What is the probability of getting exactly two heads? — 3/8
11. 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? — 14
12. 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? — 20
13. The mode of the data set: 10, 12, 15, 12, 10, 12, 15, 12 is: — 12
14. 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? — 10/21
15. In how many ways can a president, vice-president, and secretary be chosen from a group of 10 people? — 720
16. In how many ways can the letters of the word 'ENGINEERING' be arranged? — 11! / (3! * 3! * 2! * 2!)
17. How many permutations are there of the letters in the word 'APPLE'? — 60
18. How many permutations are possible for the letters of the word 'ASSASSINATION'? — 13! / (4! * 3! * 2! * 2!)
19. The median of the following data: 10, 12, 14, 16, 18, 20 is: — 15
20. The mode of the data set: 2, 3, 4, 3, 5, 3, 2, 3 is: — 3
21. In how many ways can a committee of 4 members be selected from a group of 10 people? — 210
22. 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? — 126/429
23. 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? — 24/45
24. 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? — 63
25. The mean of the first 6 positive integers is: — 3.5
26. 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? — 9/12
27. A number is selected at random from the first 20 natural numbers. What is the probability that the number is a multiple of 3? — 7/20
28. What is the value of ⁶P₂? — 30
29. The average of 5 numbers is 27. If 45 is added to the numbers, the new average is: — 36
30. The mean of 10 numbers is 30. If each number is increased by 5, the new mean is: — 35
31. 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? — 50
32. A bag contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are blue? — 49/132
33. 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? — 54
34. How many ways can 4 different colors be arranged in a circle? — 6
35. The median of the data set: 5, 2, 8, 1, 9, 4, 7 is: — 5
36. What is the probability of drawing a spade or an ace from a standard deck of 52 cards? — 18/52
37. The mean of the first 10 natural numbers is: — 5.5
38. Find the median of the following data set: 3, 7, 2, 8, 5, 9, 4. — 5
39. In how many ways can 5 distinct books be arranged on a shelf? — 120
40. What is the value of ⁵C₃? — 10
41. In how many ways can 5 people be seated in a row? — 120
42. The mean of the first 5 odd numbers is: — 5
43. How many ways can the letters of the word 'SUCCESS' be arranged? — 420
44. What is the value of ⁶C₄? — 15
45. In how many ways can 6 distinct items be arranged in a line? — 720
46. The mean of the first 5 even numbers is: — 6
47. How many different arrangements can be made from the letters of the word 'BANANA'? — 120
48. In how many ways can 4 boys and 3 girls be seated in a row so that all the girls sit together? — 144
49. Find the range of the following data: 15, 8, 22, 10, 18. — 14
50. What is the value of ⁸C₅? — 56
All One Line Questions
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