51. A dice is rolled, what is the probability of the outcome is a prime number?
एक पासा लुढ़काया जाता है, परिणाम के रूप में एक अभाज्य संख्या आने की संभावना क्या है?A. 1/2
B. 2/3
C. 5/6
D. 1/3
E. None of these

Option “A” is correct.Total event=(1, 2, 3, 4, 5, 6)Possibility of getting Prime number=(2, 3, 5)Required probability=3/6=1/2
52. Two dice are rolling simultaneously .What is the probability that the sum of the number on the two faces is divided by 5 Or 7.
दो पासा एक साथ फेंका गया हैं।क्या प्रायिकता है कि दोनों के परिणाम की संख्या 5 या 7 से विभाजित है?A. 13/36
B. 14/36
C. 11/36
D. 9/36
E. None of thesern

Option “A” is correct.
Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 5 or 7.
Then, E = {(1,4),(1,6),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(4,6),(5,2),(5,5),(6,1),(6,4)}
n(E) = 13.
Hence, P(E) = n(E)/n(S) = 13/36
53. Two dice are thrown simultaneously. What is the difference between probabilities of getting sum of the dice is divisible by 5 and the difference of the dice is divisible by 2?
एक साथ दो पासे फेंके जाते हैं। दोनों पासा पर प्राप्त होने वाले संख्याओं का योग 5 से विभाज्य होने की प्रायिकता और दोनों पासा पर प्राप्त होने वाले संख्याओं का अंतर 2 से विभाज्य होने की प्रायिकता के बीच अंतर ज्ञात करें?A. 7/36
B. 1/3
C. 1/18
D. 1/9
E. 5/36

Option “E” is correct.Possibilities of getting sum of the dice divisible by 5

  • (1,4) (2,3) (3,2) (4,1) (4,6) (5,5) (6,4) =7

Possibilities of getting difference of the dice is divisible by 2

  • (1,3) (1,5) (2,4) (2,6) (3,1) (3,5) (4,2) (4,6) (5,1) (5,3) (6,2) (6,4)=12

Required difference = (12/36)-(7/36)= 5/36
54. If two dice are thrown simultaneously, then find the difference between the possibilities of getting sum of the dice is more than 8 to that of the possibilities of getting sum of the dice is divisible by 4?
यदि दो पासा एक साथ फेंके जाते हैं, तो पासे की राशि का योग 8 से अधिक और पासे की राशि का योग का 4 से विभाज्य होने की संभावना के बीच का अंतर कितना है?A. 3
B. 4
C. 2
D. 1
E. None of these

Option “D” is correct.The possibilities of getting sum of the dice is more than 8= > (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)= > 10The possibilities of getting sum of the dice is divisible by 4= > (1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6)

= > 9

Required difference = 10 – 9 = 1
55. If two dice are thrown simultaneously, then find the probability of getting a sum of dice is divisible by 4.
यदि दो पासा उछाले जाते हैं, तो प्राप्त परिणाम के योग के 4 से विभाज्य होने की क्या प्रायिकता है?A. 4/9
B. 1/3
C. 1/4
D. 2/3
E. None of these

Option “C” is correct.Total possible = 62 = 36Possibilities of getting a sum of dice is divisible by 4= > (1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6) = 9Required probability = 9/36 = 1/4
56. If two dice are thrown simultaneously, then find the probability of getting a sum of dice is divisible by 5?
यदि दो पासे एक साथ फेंके जाते हैं, तब पासे का योग 5 से विभाज्य है, को प्राप्त करने की संभावना को ज्ञात कीजिए?A. 11/47
B. 19/62
C. 29/51
D. 7/36
E. None of these

Option “D” is correct.Total possible = 62 = 36Possibilities of getting a sum of dice is divisible by 5= > (1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4) = 7Required probability = 7/36
57. If two dice tossed, then what is the probability of getting sum divisible by 6 exactly?
यदि दो पासा उछाले जाते हैं, तो प्राप्त परिणाम के योग के 6 से विभाज्य होने की क्या प्रायिकता है?A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. None of these

Option “A” is correct.Number of events = (1,5), (2, 4), (3, 3), (4,2), (5, 1), (6, 6)Required probability = 6/36 = 1/6
58. If two dices are thrown one after other, then what is the probability of second dice gets the value more than first dice value?
यदि दो पासों को एक दूसरे के बाद फेंका गया है, तो दूसरे पासे पर पहले पासे के मान से अधिक मान को प्राप्त करने की संभावना क्या है?A. 1/2
B. 1/3
C. 1/6
D. 1/4
E. 5/12

Option “E” is correct.Total events = 36Possible events = (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6) = 15Required probability = 15/36= 5/12
59. Three 6 faced dice are thrown together, then find the probability that no two dice show the same number on them?
तीन 6 फेस वाले पासा एक साथ फेंके जाते हैं, तो इस संभावना को ज्ञात करें कि कोई भी दो पासा उन पर एक ही संख्या नहीं दिखाता है?A. 2/3
B. 3/4
C. 5/9
D. 1/2
E. 5/6

Option “C” is correct.Possibilities that 1st die can show any number = 6Possibilities that 2nd die can show any number different from 1st die = 5Possibilities that 3rd die can show any number different from 1st and 2nd dice = 4Favourable cases = 6 * 5 * 4 = 120Total cases = 63 = 216

So, probability that no two dice show the same number on them = 120/216 = 5/9
60. A dice is rolled, what is the probability of the outcome is a prime number?
एक पासे(डाइस) को उछाला जाता है, परिणाम की अभाज्य संख्या होने की प्रायिकता क्या है?A. 1/2
B. 2/3
C. 5/6
D. 1/3
E. None of these

Option “A” is correct.Total event=(1, 2, 3, 4, 5, 6)Possibility of getting Prime number=(2, 3, 5)Required probability=3/6=1/2
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