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1.
Three different dice are rolled three times. The probability that they show different numbers only two times is.
  • A.
    		 100
    243
  • C.
    		 5
    9
  • B.
    		 1
    3
  • D.
    		 107
    54
  • Answer & Explanation
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Answer : [C]
Explanation :
Total no. of cases = 63 = 216
The number of cases, when all the three numbers are distinct = 6P3
  = 6 x 5 x 4 = 120  
Required probability =
120
216
=
5
9
     
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2.
An urn contains 9 red, 7 White and 4 black balls. If two balls are drawn at random, find the probability that one is white and other red.
  • A.
    		 67
    190
  • C.
    		 71
    190
  • B.
    		 73
    190
  • D.
    		 63
    190
  • Answer & Explanation
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Answer : [D]
Explanation :
There are totally 20 balls in the bag out of which 2 balls can be drawn in 20C2 ways = 190 ways.
Out of 7 white balls one white ball can be drawn in 7C1 ways and out of 9 red balls one red ball cab be drawn in 9C1 ways.
One white and one red ball can be drawn in = 9C1 x 7C1 ways = 63 ways
Required  probability =
63
190
 
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3.
In a single throw of a die, What is the probability of getting a number greater than 4?
  • A.
    		 1  
    2  
  • C.
    		 2  
    3  
  • B.
    		 1  
    3  
  • D.
    		 1  
    4  
  • Answer & Explanation
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Answer : [B]
Explanation :
 
When a die is thrown, we have S = {1, 2, 3, 4, 5, 6}
Let E = event of getting a number greater than 4 = {5, 6}
 
  P(E) =
n(E)
n(S)
=
2
6
=
1
3
   
 
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4.
There are two boxes A and B. A contains 3 white balls and 5 black balls and box B contains 4 white and 6 black balls. One box is taken at random and one ball is picked up at random. What is the probability that the ball picked up may be a white one?
  • A.
    		 3
    20
  • C.
    		 3
    16
  • B.
    		 3
    40
  • D.
    		 31
    80
  • Answer & Explanation
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Answer : [D]
Explanation :
The required probability is the sum of (box A is selected and a white ball is picked up) + (box b is selected and a white ball is picked up)
=
1
2
x
3
8
x
1
2
x
4
10
=
3
16
+
1
5
=
31
80
   
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5.
A person throws a die, as many times till he gets 6. What is the probability that he will get 6 in the fourth throw?
  • A.
    		 53
    64
  • C.
    		 5
    36
  • B.
    		 54
    65
  • D.
    		 5
    6
  • Answer & Explanation
  • Report
Answer : [A]
Explanation :
The probability of not getting a six in the Ist throw =
5
6
 
The probability of not getting a six in the 2nd throw =
5
6
x
5
6
=
5
6
2  
The probability of not getting a six in the 4th throw =
5
6
x
5
6
x
5
6
x
1
6
=
53
64
   
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