# Probability Questions and Answers updated daily – Aptitude

Probability Questions: Solved 93 Probability Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Probability Questions

61. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

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Correct Ans:(2/7)

Explanation:

Given,In a lottery, there are 10 prizes and 25 blanks.

So, Total number of sample space = 10 + 25 = 35

=>

Event of getting prize =

=10 / 35

=

So, Total number of sample space = 10 + 25 = 35

=>

**n(S) = 35**Event of getting prize =

**n(E) = 10****Required probability = P (getting a prize) = n(E) / n(S)**=10 / 35

=

**2/7**
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62. What is the probability of getting a sum 9 from two throws of a dice?

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Correct Ans:(1/9)

Explanation:

In two throws of a dice, n(S) = (6 x 6) = 36.

Let E = event of getting a sum "9" = {(3, 6), (4, 5), (5, 4), (6, 3)}.

Therefore,

Let E = event of getting a sum "9" = {(3, 6), (4, 5), (5, 4), (6, 3)}.

Therefore,

**P(E)= n(E)/n(S)**= 4/36 =**1 / 9**
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63. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

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Correct Ans:(1 / 3)

Explanation:

Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
Therefore , n (E) = 7
Therefore P (E) = n (E) / n (S) = 7/21 = 1/3.

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64. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

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Correct Ans:(9/20)

Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

Therefore ,

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

Therefore ,

**P (E) = n (E) / n (s)**= 9/20
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65. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

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Correct Ans:3/4

Explanation:

**Solution is**

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

=>n(E) = 27

**P(E) = n(E) / n(S)**= 27 / 36 =

**3/4**

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66. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

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Correct Ans:1/3

Explanation:

**Solution is**

Total no. of Balls = n(s) = 8 + 7 + 6 = 21

Let E = event that the ball drawn is neither green nor red =event that the ball drawn is blue

n(E) = 7

P(E) = n(E) / n(S) = 7/21 =

**1/3**

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67. Two coins are tossed. What is the probability of getting atleast one tail ?

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Correct Ans:3/4

Explanation:

**Solution is**

Let H denote head and T denote tail.

When two coins are tossed, the possible cases are S = {HH, HT, TH , TT}

=> n(s) = 4

Let E be the event which denotes getting atleast one tail E = {HT , TH, TT}

=> n(E) = 3

Probability of getting atleast one tail,

P(E) = n(E) / n(S) = 3/4

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68. How many 3 digit numbers can be formed using the digits 1,3,4 and 8 ?

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Correct Ans:24

Explanation:

**Solution is**

No. of digits given to us is 4.

Nothing is mentioned about repetition of digits, so we will take it granted, the digits are not suppose to repeat.

No. of ways that 3 digit numbers can be formed = 4 P

_{3}

= 4 ! = 4 x 3 x 2

**= 24 numbers**.

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69. In how many different ways can the letters of the word 'OFFICES' be arranged ?

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Correct Ans:2520

Explanation:

**Solution is**

The word OFFICES contains O,F, F I, C, E, S contains 7 letters, in which 2 are identical.

No. of words that can formed = 7 ! / 2 !

= 7 * 6 * 5 * 4 * 3

**= 2520**

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70. In a box, there are 7 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

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Correct Ans:1/3

Explanation:

**Solution is**

No. of Balls = n(s) = 7 + 6 + 5 = 18

Let E = event that the ball drawn is neither green nor red = event that the ball drawn is blue

n(E) = 6

P(E) = n(E)/n(S)

= 6/18

**= 1/3**

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71. An unbiased dice is thrown. What is the probability of getting an odd number ?

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Correct Ans:1/2

Explanation:

**Solution is**

Sample Space , S = {1, 2, 3, 4, 5, 6}

=>n(S) = 6

E event of getting an odd number E = {1, 3, 5}

=> n(E)=3

**P(E) = n(E) / n(S)**= 3 / 6 =

**1/2**

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72. How many words can be formed with or without meaning by taking all the letters from the word COIN ?

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Correct Ans:24

Explanation:

**Solution is**

There are totally 4 letters in the word

COIN (i.e., C, O, I and N)

No. Of Words formed = 4! = 4 x 3 x 2 x 1 = 24

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73. In a party there were totaly 20 people, each person shook his hands with the other person. How many hand shakes would have taken place ?

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Correct Ans:190

Explanation:

**Solution is**

There are 20 people.

Every person has to shake hands with the other person,Which means we have to find the number of ways of choosing 2 people from the 20.

The number of ways it can happen =

**20C**

_{2}= ( 20 x 19 ) / (1 x 2) = 190
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74. Two dice are thrown simultaneously. What is the probability that the sum of the two numbers appear on the top of the dice is 9?

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Correct Ans:1/9

Explanation:

**Solution is**

Sample Space, S = { (1,1) , (1,2) , (1,3) , ... (6,6) }

=> n(S) = 6 x 6 = 36 possible cases.

E = {(x,y) / such that x+y=9}

E = {(4,5) , (5,4) , (3,6) , (6,3)}

=> n(E)=4

**Required probability:**

P(E) = n(E) / n(S)

= 4 / 36

=

**1/9**

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75. An unbiased dice is thrown. What is the probability of multiple of 3?

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Correct Ans:1/3

Explanation:

**Solution is :**

Sample Space , S = {1, 2, 3, 4, 5, 6}

**=>n(S) = 6**,

E is the event of getting multiple of 3

E = {3, 6}

**=> n(E)=2**

Probability of getting multiple of 3 is

P(E) = n(E) / n(S)

= 2 / 6

**= 1 / 3**

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76. In how many ways 3 people can be made seated in a row containing 6 seats ?

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Correct Ans:120

Explanation:

**Solution is :**

First person has got 6 ways to sit

Second person got 5 ways (since 1 seat occupied)

Third person got 4 ways.

Since all are independent

No. Of ways = 6 x 5 x 4 =

**120**

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77. Find the number of different ways of selecting 4 men from a group of 7 men ?

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Correct Ans:35

Explanation:

**Solution is :**

Total number of men = 7

Number of men to select = 4

No.of Ways to select 4 men from 7 men = 7C

_{4}

= ( 7 x 6 x 5 x 4 ) / (4 x 3 x 2 x 1)

**= 35**

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78. Two coins are tossed. What is the probability of getting exactly one tail ?

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Correct Ans:1/2

Explanation:

**Solution is**

Let H denote head and T denote tail.

When two coins are tossed, the possible cases are

S = {HH, HT, TH , TT}

**=> n(s) = 4**

Let E be the event which denotes getting exactly one tail

E = {HT , TH}

**=> n(E) = 2**

Probability of getting exactly one tail is

P(E) = n(E) / n(S)

= 2 / 4

**= 1 / 2**

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79. In a class there are some boys and 30 girls. The probability of selecting a girl is thrice the probaility of selecting a boy. Find the number of boys ?

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Correct Ans:10

Explanation:

**Solution is :**

Let the number of boys be x

Given there are 30 girls

Total number of people are (boys + girls) = x+30

Probability of selecting a girl, P(G) = 30 / (x+30)

Probability of selecting a boy, P(B) = x / (x+30)

Given P(G) = 3 x P(B)

=> 30 / (x+30) = 3x / (x+30)

=> 30 = 3x

**=> x = 10**

There are totally

**10 boys.**

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80. How many words can be formed with or without meaning by taking all the letters from the word TAKEN ?

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Correct Ans:120

Explanation:

**Solution is :**

There are totally 5 letters in the word TAKEN => T, A, K, E and N.

No. of Words formed = 5 !

= 5 x 4 x 3 x 2 x 1

**= 120**

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