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
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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
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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
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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
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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
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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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