{"id":12612,"date":"2025-09-19T10:17:01","date_gmt":"2025-09-19T09:17:01","guid":{"rendered":"https:\/\/mcqsadda.com\/?p=12612"},"modified":"2025-10-21T07:54:35","modified_gmt":"2025-10-21T06:54:35","slug":"probability-top-100-mcqs-with-answer-and-explanation","status":"publish","type":"post","link":"https:\/\/mcqsadda.com\/index.php\/2025\/09\/19\/probability-top-100-mcqs-with-answer-and-explanation\/","title":{"rendered":"Probability Top 100 MCQs With Answer and Explanation"},"content":{"rendered":"\n

1. What is the probability of getting a head when a fair coin is tossed?<\/mark><\/strong>
A) 0
B) 1\/2
C) 1
D) 2\/3
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Two outcomes \u2192 {Head, Tail}. One favorable \u2192 Probability = 1\/2.<\/p>\n\n\n\n

2. Probability of an impossible event is:
<\/strong><\/mark>A) 1
B) 0
C) 1\/2
D) Undefined
Answer:<\/strong> B) 0
Explanation:<\/strong> Impossible event has no favorable outcomes.<\/p>\n\n\n\n

3. Probability of a sure event is:<\/mark><\/strong>
A) 0
B) 1\/2
C) 1
D) Cannot be determined
Answer:<\/strong> C) 1
Explanation:<\/strong> A certain event always occurs \u2192 probability = 1.<\/p>\n\n\n\n

4. If P(E) = 0.7, then probability of not E is:<\/mark><\/strong>
A) 0.3
B) 0.5
C) 0.7
D) 1.7
Answer:<\/strong> A) 0.3
Explanation:<\/strong> P(not E) = 1 \u2013 P(E) = 1 \u2013 0.7 = 0.3.<\/p>\n\n\n\n

5. Which of the following is not a valid probability value?<\/mark><\/strong>
A) 0
B) 1\/2
C) 3\/4
D) 1.2
Answer:<\/strong> D) 1.2
Explanation:<\/strong> Probability \u2208 [0, 1].<\/p>\n\n\n\n

6. A dice is thrown. Probability of getting a number greater than 4?<\/mark><\/strong>
A) 1\/6
B) 2\/6
C) 1\/3
D) 1\/2
Answer:<\/strong> C) 1\/3
Explanation:<\/strong> Outcomes > 4 \u2192 {5, 6} \u2192 2\/6 = 1\/3.<\/p>\n\n\n\n

7. A card is drawn from a pack of 52. Probability of drawing a red card?<\/mark><\/strong>
A) 1\/4
B) 1\/2
C) 1\/3
D) 2\/3
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Red cards = 26\/52 = 1\/2.<\/p>\n\n\n\n

8. Probability of getting an odd number when a dice is thrown?<\/mark><\/strong>
A) 1\/6
B) 1\/2
C) 2\/3
D) 5\/6
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Odd numbers {1,3,5} \u2192 3\/6 = 1\/2.<\/p>\n\n\n\n

9. If a coin is tossed twice, total possible outcomes = ?<\/mark><\/strong>
A) 2
B) 3
C) 4
D) 6
Answer:<\/strong> C) 4
Explanation:<\/strong> Sample space {HH, HT, TH, TT}.<\/p>\n\n\n\n

10. Probability of getting at least one head when two coins are tossed?<\/mark><\/strong>
A) 1\/4
B) 1\/2
C) 3\/4
D) 1
Answer:<\/strong> C) 3\/4
Explanation:<\/strong> Outcomes = 4. Favourable = {HH, HT, TH} = 3. \u2192 3\/4.<\/p>\n\n\n\n

11. A number is chosen at random from 1 to 10. Probability it is prime?<\/mark><\/strong>
A) 2\/5
B) 3\/5
C) 4\/5
D) 1\/2
Answer:<\/strong> A) 2\/5
Explanation:<\/strong> Primes \u2264 10: {2,3,5,7} \u2192 4\/10 = 2\/5.<\/p>\n\n\n\n

12. If a card is drawn, probability it is a King?<\/mark><\/strong>
A) 1\/52
B) 1\/26
C) 1\/13
D) 1\/12
Answer:<\/strong> C) 1\/13
Explanation:<\/strong> Total Kings = 4. Probability = 4\/52 = 1\/13.<\/p>\n\n\n\n

13. What is the probability of getting number 7 on a dice?<\/mark><\/strong>
A) 0
B) 1\/6
C) 1\/12
D) 1\/7
Answer:<\/strong> A) 0
Explanation:<\/strong> Dice outcomes 1\u20136. 7 is impossible \u2192 probability 0.<\/p>\n\n\n\n

14. In tossing 3 coins, probability of getting all heads?<\/mark><\/strong>
A) 1\/8
B) 1\/4
C) 1\/2
D) 3\/8
Answer:<\/strong> A) 1\/8
Explanation:<\/strong> Outcomes = 8. Only 1 favorable (HHH). \u2192 1\/8.<\/p>\n\n\n\n

15. If two dice are thrown, total sample space size = ?<\/mark><\/strong>
A) 6
B) 12
C) 18
D) 36
Answer:<\/strong> D) 36
Explanation:<\/strong> Each die 6 outcomes. 6\u00d76 = 36.<\/p>\n\n\n\n

16. Probability of getting a sum of 7 on two dice?<\/mark><\/strong>
A) 1\/6
B) 1\/12
C) 1\/18
D) 1\/36
Answer:<\/strong> A) 1\/6
Explanation:<\/strong> Pairs giving 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) \u2192 6\/36 = 1\/6.<\/p>\n\n\n\n

17. Probability of drawing a black card?<\/mark><\/strong>
A) 1\/2
B) 1\/4
C) 2\/3
D) 1\/3
Answer:<\/strong> A) 1\/2
Explanation:<\/strong> Black cards = 26. Probability = 26\/52 = 1\/2.<\/p>\n\n\n\n

18. A die is rolled. Probability of a multiple of 3?<\/mark><\/strong>
A) 1\/6
B) 1\/3
C) 1\/2
D) 2\/3
Answer:<\/strong> B) 1\/3
Explanation:<\/strong> Multiples of 3 = {3,6} \u2192 2\/6 = 1\/3.<\/p>\n\n\n\n

19. If P(E) = 0.35, then P(not E) = ?<\/mark><\/strong>
A) 0.45
B) 0.55
C) 0.65
D) 0.75
Answer:<\/strong> C) 0.65
Explanation:<\/strong> 1 \u2013 0.35 = 0.65.<\/p>\n\n\n\n

20. Probability of selecting a vowel from English alphabets (A\u2013Z)?<\/mark><\/strong>
A) 5\/26
B) 21\/26
C) 1\/5
D) 5\/21
Answer:<\/strong> A) 5\/26
Explanation:<\/strong> Vowels = {A,E,I,O,U} \u2192 5\/26.<\/p>\n\n\n\n

21. A card is drawn. Probability of drawing an ace?<\/mark><\/strong>
A) 1\/52
B) 1\/13
C) 1\/26
D) 4\/13
Answer:<\/strong> B) 1\/13
Explanation:<\/strong> 4 aces in 52 cards \u2192 4\/52 = 1\/13.<\/p>\n\n\n\n

22. In a lottery of 1000 tickets, one ticket wins. If you buy 1 ticket, probability of winning = ?<\/mark><\/strong>
A) 1\/1000
B) 1\/100
C) 1\/10
D) 0
Answer:<\/strong> A) 1\/1000
Explanation:<\/strong> Favourable = 1, total = 1000 \u2192 1\/1000.<\/p>\n\n\n\n

23. A bag has 3 red and 2 black balls. Probability of drawing a red ball?<\/mark><\/strong>
A) 2\/5
B) 3\/5
C) 1\/2
D) 1\/3
Answer:<\/strong> B) 3\/5
Explanation:<\/strong> Total = 5, Red = 3 \u2192 3\/5.<\/p>\n\n\n\n

24. A die is thrown. Probability of getting even number?<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 2\/3
D) 5\/6
Answer:<\/strong> A) 1\/2
Explanation:<\/strong> Even {2,4,6} \u2192 3\/6 = 1\/2.<\/p>\n\n\n\n

25. Which is correct for any event E?<\/mark><\/strong>
A) 0 \u2264 P(E) \u2264 1
B) \u20131 \u2264 P(E) \u2264 1
C) P(E) \u2265 0 always
D) P(E) \u2265 1 always
Answer:<\/strong> A) 0 \u2264 P(E) \u2264 1
Explanation:<\/strong> Probability always lies between 0 and 1.<\/p>\n\n\n\n

26. Two dice are thrown. Probability of getting doublets (same number on both dice)?<\/mark><\/strong>
A) 1\/6
B) 1\/12
C) 1\/18
D) 1\/36
Answer:<\/strong> A) 1\/6
Explanation:<\/strong> Doublets = (1,1),(2,2)\u2026(6,6) \u2192 6 outcomes. Probability = 6\/36 = 1\/6.<\/p>\n\n\n\n

27. Probability of getting a sum of 11 on two dice?<\/mark><\/strong>
A) 1\/18
B) 1\/12
C) 1\/6
D) 1\/36
Answer:<\/strong> A) 1\/18
Explanation:<\/strong> Pairs = (5,6),(6,5) \u2192 2 outcomes. Probability = 2\/36 = 1\/18.<\/p>\n\n\n\n

28. A card is drawn. Probability it is neither king nor queen?<\/mark><\/strong>
A) 12\/13
B) 25\/26
C) 23\/26
D) 11\/13
Answer:<\/strong> A) 12\/13
Explanation:<\/strong> Kings = 4, Queens = 4 \u2192 8 total. Favorable = 52\u20138=44. Probability = 44\/52=11\/13.<\/p>\n\n\n\n

29. A coin is tossed 3 times. Probability of getting exactly 2 heads?<\/mark><\/strong>
A) 1\/8
B) 3\/8
C) 3\/4
D) 1\/2
Answer:<\/strong> B) 3\/8
Explanation:<\/strong> Outcomes = 8. Favourable = {HHT, HTH, THH} = 3. Probability = 3\/8.<\/p>\n\n\n\n

30. A card is drawn from 52. Probability it is a spade or a king?<\/mark><\/strong>
A) 4\/13
B) 17\/52
C) 16\/52
D) 13\/52
Answer:<\/strong> B) 17\/52
Explanation:<\/strong> Spades = 13, Kings = 4, but overlap (king of spades counted twice). Total favorable = 13+4\u20131=16. Probability = 16\/52 = 4\/13.<\/p>\n\n\n\n

31. Probability of getting at least one 6 in two dice throws?<\/mark><\/strong>
A) 5\/36
B) 11\/36
C) 25\/36
D) 1\/6
Answer:<\/strong> C) 25\/36
Explanation:<\/strong> P(no 6) = (5\/6)\u00d7(5\/6)=25\/36. So P(at least one 6)=1\u201325\/36=11\/36.
(\u26a0 Correction: Actually \u2192 11\/36.)<\/p>\n\n\n\n

\u2714 Correct Answer: B) 11\/36<\/strong><\/p>\n\n\n\n

32. A coin is tossed 4 times. Probability of getting all tails?<\/mark><\/strong>
A) 1\/8
B) 1\/16
C) 1\/32
D) 1\/4
Answer:<\/strong> B) 1\/16
Explanation:<\/strong> Total = 16 outcomes. Only TTTT favorable. Probability = 1\/16.<\/p>\n\n\n\n

33. A card is drawn. Probability it is a red face card?<\/mark><\/strong>
A) 3\/13
B) 3\/26
C) 6\/52
D) 12\/52
Answer:<\/strong> B) 3\/26
Explanation:<\/strong> Face cards = 12 (J,Q,K). Red face cards = 6 (\u2665\u2666). Probability = 6\/52=3\/26.<\/p>\n\n\n\n

34. Two coins are tossed. Probability of getting at least one tail?<\/mark><\/strong>
A) 1\/2
B) 3\/4
C) 1\/4
D) 2\/3
Answer:<\/strong> B) 3\/4
Explanation:<\/strong> Total outcomes = 4. Favourable = {HT,TH,TT}=3. Probability=3\/4.<\/p>\n\n\n\n

35. Probability of getting a sum of 9 on two dice?<\/mark><\/strong>
A) 1\/9
B) 1\/8
C) 1\/12
D) 1\/18
Answer:<\/strong> C) 1\/12
Explanation:<\/strong> Outcomes = (3,6),(4,5),(5,4),(6,3) \u2192 4. Probability=4\/36=1\/9.
\u2714 Correct Answer: A) 1\/9<\/strong><\/p>\n\n\n\n

36. A card is drawn. Probability it is not a heart?<\/mark><\/strong>
A) 1\/2
B) 3\/4
C) 1\/3
D) 2\/3
Answer:<\/strong> B) 3\/4
Explanation:<\/strong> Hearts=13, not hearts=39. Probability=39\/52=3\/4.<\/p>\n\n\n\n

37. Probability of getting exactly one head in 3 coin tosses?<\/mark><\/strong>
A) 1\/8
B) 2\/8
C) 3\/8
D) 4\/8
Answer:<\/strong> C) 3\/8
Explanation:<\/strong> Favourable = {HTT, THT, TTH} \u2192 3. Probability=3\/8.<\/p>\n\n\n\n

38. If two dice are thrown, probability that both numbers are even?<\/strong><\/mark>
A) 1\/4<\/mark>
B) 1\/9
C) 1\/3
D) 1\/6
Answer:<\/strong> A) 1\/4
Explanation:<\/strong> Even on each die=3\/6=1\/2. Together=(1\/2)\u00d7(1\/2)=1\/4.<\/p>\n\n\n\n

39. Probability of drawing a black queen from 52 cards?<\/mark><\/strong>
A) 1\/26
B) 1\/52
C) 1\/13
D) 1\/12
Answer:<\/strong> A) 1\/26
Explanation:<\/strong> Black queens=2. Probability=2\/52=1\/26.<\/p>\n\n\n\n

40. Two dice are thrown. Probability of getting an even sum?<\/mark><\/strong>
A) 1\/4
B) 1\/2
C) 2\/3
D) 3\/4
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Even sum occurs if both even or both odd. Half the outcomes are even \u2192 18\/36=1\/2.<\/p>\n\n\n\n

41. A coin is tossed. Probability of not getting a tail?<\/mark><\/strong>
A) 0
B) 1\/2
C) 1
D) 1\/3
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Not tail= head \u2192 probability 1\/2.<\/p>\n\n\n\n

42. Probability of drawing a king of spades?<\/mark><\/strong>
A) 1\/52
B) 1\/26
C) 1\/13
D) 1\/12
Answer:<\/strong> A) 1\/52
Explanation:<\/strong> Only one king of spades. Probability=1\/52.<\/p>\n\n\n\n

43. If 2 dice are thrown, probability of both numbers being prime?<\/mark><\/strong>
A) 1\/9
B) 1\/6
C) 1\/4
D) 1\/3
Answer:<\/strong> A) 1\/9
Explanation:<\/strong> Prime numbers on dice= {2,3,5} =3. Probability=3\/6=1\/2 each. Combined=1\/4.
Correction: Actually \u2192 (3\/6)\u00d7(3\/6)=9\/36=1\/4.
\u2714 Correct Answer: C) 1\/4<\/strong><\/p>\n\n\n\n

44. Probability of getting 2 or 3 on a dice?<\/mark><\/strong>
A) 1\/6
B) 2\/6
C) 1\/3
D) 1\/2
Answer:<\/strong> B) 2\/6 = 1\/3
Explanation:<\/strong> Favourable={2,3}. Probability=2\/6=1\/3.<\/p>\n\n\n\n

45. A card is drawn. Probability that it is neither red nor a king?<\/mark><\/strong>
A) 3\/4
B) 11\/13
C) 12\/13
D) 25\/26
Answer:<\/strong> B) 11\/13
Explanation:<\/strong> Red cards=26, kings=4, overlap=2 (red kings). Total=28. Favorable=24. Probability=24\/52=6\/13.
\u2714 Correct Answer: 6\/13 (not in given options)<\/strong><\/p>\n\n\n\n

46. Two dice thrown. Probability of getting sum \u2264 4?<\/mark><\/strong>
A) 1\/9
B) 1\/6
C) 1\/12
D) 1\/18
Answer:<\/strong> B) 1\/6
Explanation:<\/strong> Favourable sums=2,3,4. Outcomes=(1,1),(1,2),(2,1),(1,3),(2,2),(3,1) \u21926. Probability=6\/36=1\/6.<\/p>\n\n\n\n

47. Probability of drawing a non-face card?<\/mark><\/strong>
A) 10\/13
B) 11\/13
C) 3\/4
D) 2\/3
Answer:<\/strong> A) 10\/13
Explanation:<\/strong> Face cards=12. Non-face=40. Probability=40\/52=10\/13.<\/p>\n\n\n\n

48. A card is drawn. Probability it is a diamond or club?<\/mark><\/strong>
A) 1\/2
B) 1\/4
C) 1\/3
D) 2\/3
Answer:<\/strong> A) 1\/2
Explanation:<\/strong> Diamonds=13, clubs=13 \u2192 26. Probability=26\/52=1\/2.<\/p>\n\n\n\n

49. Probability of getting a sum of 5 on two dice?<\/mark><\/strong>
A) 1\/9
B) 1\/12
C) 1\/18
D) 1\/36
Answer:<\/strong> B) 1\/12
Explanation:<\/strong> Outcomes: (1,4),(2,3),(3,2),(4,1)=4. Probability=4\/36=1\/9.
\u2714 Correct Answer: A) 1\/9<\/strong><\/p>\n\n\n\n

50. If two coins are tossed, probability of getting one head and one tail?<\/mark><\/strong>
A) 1\/4
B) 1\/2
C) 3\/4
D) 2\/3
Answer:<\/strong> B) 1\/2
Explanation:<\/strong> Outcomes= {HH,HT,TH,TT}. Favorable={HT,TH}=2. Probability=2\/4=1\/2.<\/p>\n\n\n\n

51. If P(A) = 0.5, P(B) = 0.4 and A & B are independent, find P(A \u2229 B).<\/mark><\/strong>
A) 0.1
B) 0.2
C) 0.25
D) 0.9
Answer:<\/strong> B) 0.2
Explanation:<\/strong> For independent events \u2192 P(A \u2229 B) = P(A) \u00d7 P(B) = 0.5 \u00d7 0.4 = 0.2.<\/p>\n\n\n\n

52. If P(A) = 0.7, P(B) = 0.6, P(A \u2229 B) = 0.5, then P(A \u222a B) = ?<\/mark><\/strong>
A) 0.8
B) 0.9
C) 1.2
D) 0.7
Answer:<\/strong> A) 0.8
Explanation:<\/strong> P(A \u222a B) = P(A)+P(B)\u2013P(A \u2229 B) = 0.7+0.6\u20130.5=0.8.<\/p>\n\n\n\n

53. Two independent events A and B have probabilities 0.6 and 0.5. Probability that both occur?<\/mark><\/strong>
A) 0.1
B) 0.2
C) 0.3
D) 0.25
Answer:<\/strong> C) 0.3
Explanation:<\/strong> P(A \u2229 B) = 0.6\u00d70.5 = 0.3.<\/p>\n\n\n\n

54. If P(A) = 0.4, P(B) = 0.5, and A, B independent, probability that neither occurs?<\/mark><\/strong>
A) 0.1
B) 0.2
C) 0.3
D) 0.6
Answer:<\/strong> D) 0.6
Explanation:<\/strong> P(A \u222a B) = 0.4+0.5\u20130.2=0.7. So P(none) = 1\u20130.7=0.3.
\u2714 Correct Answer: C) 0.3<\/strong><\/p>\n\n\n\n

55. If P(A) = 0.3, P(B) = 0.2, and A,B mutually exclusive, P(A \u222a B) = ?<\/mark><\/strong>
A) 0.1
B) 0.3
C) 0.5
D) 0.6
Answer:<\/strong> C) 0.5
Explanation:<\/strong> Mutually exclusive \u2192 P(A \u2229 B)=0. So P(A \u222a B)=0.3+0.2=0.5.<\/p>\n\n\n\n

56. If P(A) = 0.4, P(B) = 0.5, P(A \u2229 B) = 0.2, then P(A|B) = ?<\/mark><\/strong>
A) 0.2
B) 0.4
C) 0.6
D) 0.7
Answer:<\/strong> C) 0.6
Explanation:<\/strong> P(A|B) = P(A \u2229 B)\/P(B) = 0.2\/0.5=0.4.
\u2714 Correct Answer: B) 0.4<\/strong><\/p>\n\n\n\n

57. If two dice are thrown, find P(sum is even | first die shows 3).<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 2\/3
D) 5\/6
Answer:<\/strong> A) 1\/2
Explanation:<\/strong> If first die=3 (odd), second die must be odd for sum even. Half the outcomes \u2192 3\/6=1\/2.<\/p>\n\n\n\n

58. A bag has 3 red, 2 black. One ball drawn. Probability red given it is not black?<\/mark><\/strong>
A) 1
B) 3\/5
C) 1\/2
D) 2\/3
Answer:<\/strong> A) 1
Explanation:<\/strong> If not black \u2192 must be red. Probability = 1.<\/p>\n\n\n\n

59. A coin tossed twice. Find P(first toss is head | exactly one head occurs).<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 2\/3
D) 1\/4
Answer:<\/strong> A) 1\/2
Explanation:<\/strong> Exactly one head outcomes {HT,TH}. Given condition \u2192 2 outcomes. Favourable {HT}. Probability=1\/2.<\/p>\n\n\n\n

60. A bag has 2 white, 3 red, 5 black. One ball drawn. P(red|not black)?<\/mark><\/strong>
A) 1\/5
B) 1\/2
C) 3\/5
D) 3\/7
Answer:<\/strong> D) 3\/7
Explanation:<\/strong> Not black \u2192 {2W,3R}=5. Red among them=3. Probability=3\/5.
\u2714 Correct Answer: C) 3\/5<\/strong><\/p>\n\n\n\n

61. If P(A) = 0.5, P(B) = 0.3, P(A \u2229 B) = 0.2, find P(A|B).<\/mark><\/strong>
A) 2\/3
B) 1\/2
C) 1\/3
D) 1\/4
Answer:<\/strong> A) 2\/3
Explanation:<\/strong> P(A|B)=P(A \u2229 B)\/P(B)=0.2\/0.3=2\/3.<\/p>\n\n\n\n

62. Two cards drawn without replacement from 52. Find P(both aces).<\/mark><\/strong>
A) 1\/169
B) 1\/221
C) 1\/1326
D) 1\/26
Answer:<\/strong> B) 1\/221
Explanation:<\/strong> P= (4\/52)\u00d7(3\/51) = 12\/2652 = 1\/221.<\/p>\n\n\n\n

63. From 1\u201320, one number chosen. Find P(multiple of 4 | even).<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 2\/5
D) 1\/4
Answer:<\/strong> B) 1\/3
Explanation:<\/strong> Even numbers=10. Multiples of 4 among them= {4,8,12,16,20}=5. Probability=5\/10=1\/2.
\u2714 Correct Answer: A) 1\/2<\/strong><\/p>\n\n\n\n

64. If P(A) = 0.6, P(B) = 0.5, and P(A \u2229 B)=0.3, are A and B independent?<\/mark><\/strong>
A) Yes
B) No
C) Sometimes
D) Can\u2019t say
Answer:<\/strong> A) Yes
Explanation:<\/strong> Independence check: P(A)\u00d7P(B)=0.6\u00d70.5=0.3 = P(A \u2229 B). So independent.<\/p>\n\n\n\n

65. A bag has 3 white, 2 red. Two balls drawn without replacement. Find P(both white).<\/mark><\/strong>
A) 1\/5
B) 1\/10
C) 1\/3
D) 3\/10
Answer:<\/strong> D) 3\/10
Explanation:<\/strong> P= (3\/5)\u00d7(2\/4)=6\/20=3\/10.<\/p>\n\n\n\n

66. If a card is drawn, probability that it is king given that it is a face card?<\/mark><\/strong>
A) 1\/12
B) 1\/3
C) 1\/4
D) 1\/13
Answer:<\/strong> B) 1\/3
Explanation:<\/strong> Face cards=12 (J,Q,K). Kings=4. Probability=4\/12=1\/3.<\/p>\n\n\n\n

67. Two dice thrown. Probability that sum is 9 given first die is 4?<\/mark><\/strong>
A) 1\/6
B) 1\/3
C) 1\/2
D) 1\/12
Answer:<\/strong> A) 1\/6
Explanation:<\/strong> If first=4, second must=5. One favourable out of 6 \u2192 1\/6.<\/p>\n\n\n\n

68. A bag has 2 red, 3 green, 5 blue. One ball drawn. P(green | not blue)?<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 3\/5
D) 3\/8
Answer:<\/strong> B) 1\/3
Explanation:<\/strong> Not blue = 5 balls (2R+3G). Green among them=3. Probability=3\/5.
\u2714 Correct Answer: C) 3\/5<\/strong><\/p>\n\n\n\n

69. A card drawn. Find P(king or queen | face card).<\/mark><\/strong>
A) 1\/2
B) 2\/3
C) 1\/3
D) 1\/4
Answer:<\/strong> B) 2\/3
Explanation:<\/strong> Face cards=12. Kings+Queens=8. Probability=8\/12=2\/3.<\/p>\n\n\n\n

70. A coin is tossed thrice. Find P(exactly 2 heads | at least 1 head).<\/mark><\/strong>
A) 3\/8
B) 3\/7
C) 1\/3
D) 1\/2
Answer:<\/strong> B) 3\/7
Explanation:<\/strong> Total outcomes=8. At least one head=7 outcomes. Exactly 2 heads=3 outcomes. Probability=3\/7.<\/p>\n\n\n\n

71. A die is rolled. Find P(even number | prime number).<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 1\/4
D) 2\/3
Answer:<\/strong> C) 1\/4
Explanation:<\/strong> Primes on die={2,3,5}. Even among them={2}. Probability=1\/3.
\u2714 Correct Answer: B) 1\/3<\/strong><\/p>\n\n\n\n

72. From 1\u201310, number chosen. P(odd | not prime)?<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 1\/4
D) 2\/5
Answer:<\/strong> D) 2\/5
Explanation:<\/strong> Non-primes= {1,4,6,8,9,10} = 6. Odd among them= {1,9}=2. Probability=2\/6=1\/3.
\u2714 Correct Answer: B) 1\/3<\/strong><\/p>\n\n\n\n

73. A box has 2 defective, 8 good bulbs. If 1 picked, find P(defective | not good)?<\/mark><\/strong>
A) 0
B) 1
C) 1\/5
D) 2\/5
Answer:<\/strong> B) 1
Explanation:<\/strong> If not good \u2192 must be defective. Probability=1.<\/p>\n\n\n\n

74. If a coin is tossed thrice, find P(first toss head | total heads = 2).<\/mark><\/strong>
A) 1\/2
B) 1\/3
C) 2\/3
D) 1\/4
Answer:<\/strong> C) 2\/3
Explanation:<\/strong> Exactly 2 heads outcomes= {HHT,HTH,THH}. First head in 2 of them. Probability=2\/3.<\/p>\n\n\n\n

75. (Bayes\u2019 theorem) A bag has 2 red, 3 green. Another has 4 red, 5 green. One bag chosen at random, 1 ball drawn and it is red. Probability it came from first bag?<\/mark><\/strong>
A) 2\/7
B) 3\/7
C) 4\/7
D) 5\/7
Answer:<\/strong> B) 3\/7
Explanation:<\/strong><\/p>\n\n\n\n