71. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

1. 1. 1

      4

   
   
   

   2. 3

      8

   
   
   

   3. 1

      2

   
   
   

   4. 3

      4

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Number of favourable cases are given by
   H H H T
   H H T H
   H T H H
   T H H H
   Total number of cases = ²C₁ × ²C₁ × ²C₁ × ²C₁ = 16
   

   ∴ Probablity =		4	=	1
   		16		4

   
   

   Correct Option: A

   Number of favourable cases are given by
   H H H T
   H H T H
   H T H H
   T H H H
   Total number of cases = ²C₁ × ²C₁ × ²C₁ × ²C₁ = 16
   

   ∴ Probablity =		4	=	1
   		16		4

   
   

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72. A box contains 20 defective items and 80 nondefective items. If two items are selected at random without replacement, what will be the probability that both items are defective?

1. 1. 1

      5

   
   
   

   2. 1

      25

   
   
   

   3. 20

      99

   
   
   

   4. 19

      495

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   P(Both defective) =	N(Both defective)
   	Sample space

   
   

   =		20C2	=	19
   		100C2		495

   
   

   Correct Option: D

   P(Both defective) =	N(Both defective)
   	Sample space

   
   

   =		20C2	=	19
   		100C2		495

   
   

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73. A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?

1. 1. 1

      9

   
   
   

   2. 5

      36

   
   
   

   3. 1

      4

   
   
   

   4. 3

      4

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   The number of ways of coming 8 and 9 are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3) Total ways = 9
   So probability of coming 8 and 9 are
   

   =		9	=	9
   		6 × 6		36

   
   So probability of not coming these
   

   = 1 -		9	=	3
   		36		4

   
   

   Correct Option: D

   The number of ways of coming 8 and 9 are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3) Total ways = 9
   So probability of coming 8 and 9 are
   

   =		9	=	9
   		6 × 6		36

   
   So probability of not coming these
   

   = 1 -		9	=	3
   		36		4

   
   

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74. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

1. 1. 0.0036

   
   
   

   2. 0.1937

   
   
   

   3. 0.2234

   
   
   

   4. 0.3874

   
   
   

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1. View Hint View Answer Discuss in Forum

   Probability of defective item =	10	= 0.1
   	100

   
   Probability of not defective item = 1 – 0.1 = 0.9
   So, probability that exactly 2 of the chosen items are defective
   = ¹⁰C₂ (0.1)² (0.9)⁸ = 0.1937.

   Correct Option: B

   Probability of defective item =	10	= 0.1
   	100

   
   Probability of not defective item = 1 – 0.1 = 0.9
   So, probability that exactly 2 of the chosen items are defective
   = ¹⁰C₂ (0.1)² (0.9)⁸ = 0.1937.

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75. From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?

1. 1. 1

      26

   
   
   

   2. 1

      52

   
   
   

   3. 1

      169

   
   
   

   4. 1

      221

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Probability of both cards being king
   

   =		4	×	3	=	1
   		52		51		221

   
   

   Correct Option: D

   Probability of both cards being king
   

   =		4	×	3	=	1
   		52		51		221

   
   

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