61. Three coins are tossed. What is the probability of getting exactly two heads?
तीन सिक्के उछाले जाते हैं। दो हेड आने की प्रायिकता क्या है?A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. None of these

Option “B” is correct.Total events =(HHH, HHT, THT, HTH, THH, HTT, TTH, TTT)=8Exactly two heads=(HHT, HTH, THH)=3Required probability=3/8
62. Three coins are tossed. What is the probability of getting exactly two tails?
तीन सिक्के उछाले गए हैं। वास्तव में दो पट(टेल्स) प्राप्त होने की संभावना क्या है?A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. None of these

Option “B” is correct.Total event=(HHH, HHT, HTH, THH, THT, HTT, TTH, TTT)=8Possible ways =(THT, HTT, TTH)=3Required probability=3/8
63. Two unbiased coins are taken. They are tossed together for 5 times. What is the probability that both of them showed different outcomes in at least 4 throws?
दो अनभिनत सिक्के लिए गए हैं। उन्हें 5 बार साथ-साथ उछाला गया है। क्या संभावना है कि उन दोनों ने कम से कम 4 फेंक में अलग-अलग परिणाम दिखाए?A. 5/16
B. 7/16
C. 1/16
D. 1/4
E. None of these

Option “E” is correct.When two coins are thrown together, possible outcomes are(H, H) (T, T) (T, H) (H, T)Probability of same outcome = 2/4 = 1/2Probability of different outcome = 1/2Probability of different outcomes in at least 4 throws = 5C4 x (1/2)5 + 5C5 x (1/2)5 = 3/16
64. Two unbiased coins are tossed. What is the probability of getting exactly two heads?
दो निष्पक्ष सिक्के उछाले जाते हैं। ठीक ठीक दो हेड होने की संभावना क्या है?A. 1/2
B. 1/3
C. 1/4
D. 3/4
E. None of these

Option “C” is correct.Total event={HH, HT, TH, TT}=4Possible=HH=1Required probability=1/4
65. A coin is thrown 3 times. What is the probability that at least one head is obtained?
एक सिक्का 3 बार फेंका जाता है। क्या संभावना है कि कम से कम एक हेड प्राप्त हो?A. 5/8
B. 3/4
C. 7/8
D. 1/2
E. 3/8

Option “C” is correct.Possible event = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}Required probability= 1-1/8 =7/8
66. A purse contains 4 silver coins, 6 gold coins and x bronze coins are there. If two coins are taken at random, then the probability of taking 2 gold coins is 5/77, then find the total number of coins in the purse?
एक पर्स में 4 चांदी के सिक्के, 6 सोने के सिक्के और x कांस्य के सिक्के हैं। यदि दो सिक्के यादृच्छिक रूप से लिए जाते हैं, तो 2 सोने के सिक्के लेने की प्रायिकता 5/77 है, तो पर्स में सिक्कों की कुल संख्या ज्ञात कीजिए?A. 22
B. 20
C. 25
D. 27
E. None of these

Option “A” is correct.Total number of balls=4+6+x=10+xProbability=6C2/(10+x)C2=5/776*5/(10+x)*(9+x)=5/77x2+19x-372=0(x+31)(x-12)=0

x=12

Total number of coins=10+12=22
67. If the coin is tossed 5 times then what is the probability of getting two tails?
यदि सिक्का 5 बार उछाला गया है, तो दो पट्ट प्राप्त करने की क्या संभावना है?A. 1/4
B. 5/16
C. 3/8
D. 1/16
E. None of these

Option “B” is correct.Required probability = 5C2/25    = 10/32= 5/16
68. If two coins are tossed together for 4 times, then find the probability of getting exactly one tail.
यदि दो सिक्कों को एक साथ 4 बार उछाला जाता है, तो ठीक एक पट आने की प्रायिकता ज्ञात कीजिए।A. 1/8
B. 5/8
C. 1/2
D. 1/4
E. None of these

Option “C” is correct.The possible outcome of the two coins are tossed together = (H, H), (H, T), (T, H), (T, T) = 4The possibility of getting exactly one tail = (H, T), (T, H) = 2The probability of getting exactly one tail = 2/4 = 1/2
69. If two coins are tossed, then find the sum of the probability of getting at most one head and the probability of getting exactly two tails
यदि दो सिक्कों को उछाला जाता है, तो अधिक से अधिक एक चित्त आने की प्रायिकता और ठीक दो पट आने की प्रायिकता का योग ज्ञात कीजिए।A. 1
B. 3/8
C. 1/4
D. 5/8
E. None of these

Option “A” is correct.The possibleoutcome of the two coins are tossed together = (H, H), (H, T), (T, H), (T, T) = 4The possibility of getting at most one head = (H, T), (T, H), (T, T) = 3The possibility of getting exactly two tails = (T, T) = 1Required sum = 3/4 + 1/4 = 1
70. Three coins are tossed. What is the probability of getting exactly two tails?
तीन सिक्के उछाले जाते हैं। ठीक दो पट (Tail) आने की प्रायिकता क्या है?A. 1/4
B. 3/8
C. 1/2
D. 5/8
E. None of these

Option “B” is correct.Total event=(HHH, HHT, HTH, THH, THT, HTT, TTH, TTT)=8Possible ways =(THT, HTT, TTH)=3Required probability=3/8
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