Probability, Permutation and Combination - One Line Questions

1. What is the probability of drawing two kings from a deck of 52 cards without replacement? — (4/52) * (3/51)
2. A bag contains 5 green and 7 yellow balls. If two balls are drawn without replacement, what is the probability that both are green? — (5/12) * (4/11)
3. What is the probability of an event that is certain to occur? — 1
4. What is the value of 0!? — 1
5. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent events, what is P(A ∩ B)? — 0.12
6. If P(A) = 0.6, P(B) = 0.5, and P(A ∪ B) = 0.8, what is P(A ∩ B)? — 0.3
7. If P(A) = 0.5, what is the probability of the complement of A, P(A')? — 0.5
8. If P(A) = 0.6 and P(B) = 0.7, and P(A ∩ B) = 0.4, what is P(A ∪ B)? — 0.9
9. What is the probability of an impossible event? — 0
10. A fair coin is tossed once. What is the probability of getting a head? — 1/2
11. A coin is tossed 5 times. What is the probability of getting at least one head? — 31/32
12. Two dice are rolled simultaneously. What is the probability of getting a sum of 7? — 6/36
13. What is the probability that a randomly selected year is a leap year? — 1/4
14. What is the probability that a randomly chosen 3-digit number is divisible by 5? — 1/5
15. From a deck of 52 cards, one card is drawn. What is the probability of drawing an Ace? — 4/52
16. A fair die is rolled. What is the probability of getting a number greater than 4? — 2/6
17. What is the probability that a year chosen at random contains 53 Sundays? — 2/7
18. In how many ways can a committee of 3 people be chosen from a group of 5 people? — 10
19. What is the probability that a number selected from 1 to 30 is a multiple of 3? — 10/30
20. In how many ways can the first three positions in a race be filled by 10 contestants? — 720
21. How many ways can the letters of the word 'ENGINEERING' be arranged? — 11! / (3! * 3! * 2! * 1!)
22. What is the total number of possible outcomes when rolling two distinct dice? — 36
23. What is the value of 5! (5 factorial)? — 120
24. How many ways can the letters of the word 'APPLE' be arranged? — 60
25. How many ways can a team of 5 players be selected from 12 players? — 12C5
26. In how many ways can 5 men and 2 women be seated in a row so that the two women are always together? — 1440
27. How many ways can a president, vice-president, and treasurer be selected from a club of 15 members? — 15P3
28. How many ways can 4 people be arranged in a line? — 24
29. If nCr = 10 and n = 5, what is r? — 2 or 3
30. What is the total number of possible outcomes when tossing three fair coins? — 8
31. If nPr = 720 and n = 6, what is r? — 3
32. A letter is chosen at random from the word 'ASSASSINATION'. What is the probability that it is an 'S'? — 4/13
33. A fair die is rolled twice. What is the probability of getting a sum of 10? — 3/36
34. What is the probability of drawing a black card or a king from a standard deck of 52 cards? — 28/52
35. A bag contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that it is red? — 4/10
36. What is the probability of picking a prime number from the integers 1 to 10? — 4/10
37. How many diagonals does a polygon with 10 sides have? — 45
38. What is the probability of getting exactly 2 heads in 4 coin tosses? — 4C2 * (1/2)^4
39. How many ways can 5 distinct books be arranged on a shelf? — 120
40. How many ways can 5 different prizes be distributed among 5 students, if each student gets one prize? — 120
41. What is the probability of selecting a vowel from the letters of the word 'EDUCATION'? — 5/9
42. How many permutations are possible with the letters of the word 'SUCCESS'? — 7!/3!2!
43. If nC(r-1) : nCr : nC(r+1) = 1:2:3, find n. — 7
44. What is the probability of selecting a number divisible by 7 from the integers 1 to 50? — 7/50
45. How many distinct arrangements are there of the letters in the word 'BANANA'? — 60
46. What is the total number of ways to arrange 3 men and 3 women in a row such that all men sit together? — 144
47. In how many ways can 6 students be seated in a row if two specific students must sit together? — 144
48. How many ways can a committee of 4 men and 3 women be formed from 7 men and 5 women? — 7C4 * 5C3
49. What is the probability of drawing a red ball or a blue ball from a bag containing 5 red, 3 blue, and 2 green balls? — 8/10
50. What is the number of permutations of n distinct objects taken r at a time, denoted as nPr? — n! / (n-r)!
All One Line Questions
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