03 - Question bank- Probability - Class 10 - Maths Class 10 Notes | EduRev

Crash Course for Class 10 Maths by Let's tute

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Class 10 : 03 - Question bank- Probability - Class 10 - Maths Class 10 Notes | EduRev

 Page 1


Probability 
 
 
 
1) A bag contains a green ball, a white ball and a black ball all balls being of the 
same shape and size.  Rohan takes a ball from the bag without looking into it.  
What is the probability that he takes out a black ball?? 
Solution: 
 Since Rohan takes the ball out without looking into it. So it is equally likely  
that he takes out any one of them.  
Since there is only one black ball,  
Let B be the event that we get a black ball  
The number of favourable outcomes = 1 
The number of possible outcomes = 3 
P(B)=  
The number of favourable outcomes
The number of possible outcomes
 
1
P(B) =  
3
 
 
2)  Suppose, we throw a die once,  
(i) What is the probability that we get a number greater than 3  
(ii) What is the probability of getting a number less than  or equal to 3? 
Solution: 
 Let E be an event that we get a number greater than 3.  
 The possibilities according to given condition are 4, 5, 6.  
 The total possibilities are 1, 2, 3,4,5,6.  
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
 
 Let D be the event that we get a number less than or equal to 3. 
 The given possibilities are 1, 2, 3.  
 The total possibilities are 1, 2, 3, 4, 5, 6.  
Page 2


Probability 
 
 
 
1) A bag contains a green ball, a white ball and a black ball all balls being of the 
same shape and size.  Rohan takes a ball from the bag without looking into it.  
What is the probability that he takes out a black ball?? 
Solution: 
 Since Rohan takes the ball out without looking into it. So it is equally likely  
that he takes out any one of them.  
Since there is only one black ball,  
Let B be the event that we get a black ball  
The number of favourable outcomes = 1 
The number of possible outcomes = 3 
P(B)=  
The number of favourable outcomes
The number of possible outcomes
 
1
P(B) =  
3
 
 
2)  Suppose, we throw a die once,  
(i) What is the probability that we get a number greater than 3  
(ii) What is the probability of getting a number less than  or equal to 3? 
Solution: 
 Let E be an event that we get a number greater than 3.  
 The possibilities according to given condition are 4, 5, 6.  
 The total possibilities are 1, 2, 3,4,5,6.  
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
 
 Let D be the event that we get a number less than or equal to 3. 
 The given possibilities are 1, 2, 3.  
 The total possibilities are 1, 2, 3, 4, 5, 6.  
Probability 
 
 
 
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
   
 
3) A single card is drawn from a well shuffled pack of 52 cards.  
 Calculate the probability that the card is 
 (i)  a King 
 (ii) not a king 
Solution:  
(i) Let E be the event that the card is a King.  
 There are 4 kings in a deck  
 The number of favourable outcomes = 4 
 The number of possible outcomes = 52 
 P (E) = 
The number of favourable outcomes
The number of possible outcomes
 
         =  
4
52
 
 
1
P(E) =  
13
 
(ii) Let D be the event that the card is not a king  
 Hence D =  E  
 Therefore,  
 P( E )  = 1- P(E) 
   = 1- 
1
13
 
 P( E ) =  
12
13
      
12
P(D) =  
13
 
Page 3


Probability 
 
 
 
1) A bag contains a green ball, a white ball and a black ball all balls being of the 
same shape and size.  Rohan takes a ball from the bag without looking into it.  
What is the probability that he takes out a black ball?? 
Solution: 
 Since Rohan takes the ball out without looking into it. So it is equally likely  
that he takes out any one of them.  
Since there is only one black ball,  
Let B be the event that we get a black ball  
The number of favourable outcomes = 1 
The number of possible outcomes = 3 
P(B)=  
The number of favourable outcomes
The number of possible outcomes
 
1
P(B) =  
3
 
 
2)  Suppose, we throw a die once,  
(i) What is the probability that we get a number greater than 3  
(ii) What is the probability of getting a number less than  or equal to 3? 
Solution: 
 Let E be an event that we get a number greater than 3.  
 The possibilities according to given condition are 4, 5, 6.  
 The total possibilities are 1, 2, 3,4,5,6.  
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
 
 Let D be the event that we get a number less than or equal to 3. 
 The given possibilities are 1, 2, 3.  
 The total possibilities are 1, 2, 3, 4, 5, 6.  
Probability 
 
 
 
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
   
 
3) A single card is drawn from a well shuffled pack of 52 cards.  
 Calculate the probability that the card is 
 (i)  a King 
 (ii) not a king 
Solution:  
(i) Let E be the event that the card is a King.  
 There are 4 kings in a deck  
 The number of favourable outcomes = 4 
 The number of possible outcomes = 52 
 P (E) = 
The number of favourable outcomes
The number of possible outcomes
 
         =  
4
52
 
 
1
P(E) =  
13
 
(ii) Let D be the event that the card is not a king  
 Hence D =  E  
 Therefore,  
 P( E )  = 1- P(E) 
   = 1- 
1
13
 
 P( E ) =  
12
13
      
12
P(D) =  
13
 
Probability 
 
4)  Two players, Rahul and Rohit are playing a Badminton match.   
The probability of Rahul winning the match is 0.37.  
What is the probability of  Rohit winning the match? 
Solution: 
 Let E denote the event that Rahul wins the match and  
 D denote the event that Rohit wins the match. 
 Given that, 
 Probability that Rahul wins the match = P(E) = 0.37 
 Therefore 
 Probability that Rohit wins the match  = P(D) = 1- P(E) 
 Probability that Rohit wins the match  = P(D) = 1- 0.37 = 0.63  
 
 
5) There are 60 students in class XII of a school of whom 35 are boys.  
 The class teacher has to select a class monitor. She tell the students to write 
 their names on an identical piece of paper.  Then she put all the chits in a  
 bowl and stirs it thoroughly and draws a card at random from the bowl.  
 What is the probability that the name written on the chit is that of  
 (i) a girl (ii) a boy? 
Solution: 
 The number of possible outcomes = 60 
 (i)  
 Let G be the event that the name drawn is that of a girl  
 The number of favourable outcomes = 25 
 P(G) = 
The number of favourable outcomes
The number of possible outcomes 
 
 P(G) = 
25
60
= 
5
12
 
  
5
P(G) =
12
 
  (ii) 
 Let B be the event that the name drawn is that of a boy  
 P(B) = 1 – P(G) 
Page 4


Probability 
 
 
 
1) A bag contains a green ball, a white ball and a black ball all balls being of the 
same shape and size.  Rohan takes a ball from the bag without looking into it.  
What is the probability that he takes out a black ball?? 
Solution: 
 Since Rohan takes the ball out without looking into it. So it is equally likely  
that he takes out any one of them.  
Since there is only one black ball,  
Let B be the event that we get a black ball  
The number of favourable outcomes = 1 
The number of possible outcomes = 3 
P(B)=  
The number of favourable outcomes
The number of possible outcomes
 
1
P(B) =  
3
 
 
2)  Suppose, we throw a die once,  
(i) What is the probability that we get a number greater than 3  
(ii) What is the probability of getting a number less than  or equal to 3? 
Solution: 
 Let E be an event that we get a number greater than 3.  
 The possibilities according to given condition are 4, 5, 6.  
 The total possibilities are 1, 2, 3,4,5,6.  
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
 
 Let D be the event that we get a number less than or equal to 3. 
 The given possibilities are 1, 2, 3.  
 The total possibilities are 1, 2, 3, 4, 5, 6.  
Probability 
 
 
 
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
   
 
3) A single card is drawn from a well shuffled pack of 52 cards.  
 Calculate the probability that the card is 
 (i)  a King 
 (ii) not a king 
Solution:  
(i) Let E be the event that the card is a King.  
 There are 4 kings in a deck  
 The number of favourable outcomes = 4 
 The number of possible outcomes = 52 
 P (E) = 
The number of favourable outcomes
The number of possible outcomes
 
         =  
4
52
 
 
1
P(E) =  
13
 
(ii) Let D be the event that the card is not a king  
 Hence D =  E  
 Therefore,  
 P( E )  = 1- P(E) 
   = 1- 
1
13
 
 P( E ) =  
12
13
      
12
P(D) =  
13
 
Probability 
 
4)  Two players, Rahul and Rohit are playing a Badminton match.   
The probability of Rahul winning the match is 0.37.  
What is the probability of  Rohit winning the match? 
Solution: 
 Let E denote the event that Rahul wins the match and  
 D denote the event that Rohit wins the match. 
 Given that, 
 Probability that Rahul wins the match = P(E) = 0.37 
 Therefore 
 Probability that Rohit wins the match  = P(D) = 1- P(E) 
 Probability that Rohit wins the match  = P(D) = 1- 0.37 = 0.63  
 
 
5) There are 60 students in class XII of a school of whom 35 are boys.  
 The class teacher has to select a class monitor. She tell the students to write 
 their names on an identical piece of paper.  Then she put all the chits in a  
 bowl and stirs it thoroughly and draws a card at random from the bowl.  
 What is the probability that the name written on the chit is that of  
 (i) a girl (ii) a boy? 
Solution: 
 The number of possible outcomes = 60 
 (i)  
 Let G be the event that the name drawn is that of a girl  
 The number of favourable outcomes = 25 
 P(G) = 
The number of favourable outcomes
The number of possible outcomes 
 
 P(G) = 
25
60
= 
5
12
 
  
5
P(G) =
12
 
  (ii) 
 Let B be the event that the name drawn is that of a boy  
 P(B) = 1 – P(G) 
Probability 
 
  
 
P(B) = 1 - 
5
12
 
7
P(B) =
12
 
5) A bas contains only yellow marbles. Avinash takes one marble without looking  
 into the bag. What is the probability that he takes out  
 (i) a pink marble (ii) a black marble 
Solution: 
 (i)  
 Let P be the event that a pink marble is taken out 
 Since the bag contains no pink marbles 
 The number of favourable outcomes = 0 
 P (P) = 
The number of favourable outcomes
The number of possible outcomes 
 
 P(P) =0  
 (ii) 
 Let Y be the event that a black marble is taken out 
 Since the bag only contains yellow marbles & no black marble. 
    ( )   
 
6) A box contains 8 green marbles, 3 white marbles and 9 orange marbles.  
 One marble is taken out of the box at random. What is the probability that 
 the marble taken out will be  (i) green   (ii) not white   (iii) orange.  
Solution:  
 The number of possible outcomes = 20 
 (i)  
  Let G be the event that a green marble is taken out.  
  The number of favourable outcomes = 8 
  P (G) = 
The number of favourable outcomes
The number of possible outcomes 
 
  P (G) = 
8
20
 
Page 5


Probability 
 
 
 
1) A bag contains a green ball, a white ball and a black ball all balls being of the 
same shape and size.  Rohan takes a ball from the bag without looking into it.  
What is the probability that he takes out a black ball?? 
Solution: 
 Since Rohan takes the ball out without looking into it. So it is equally likely  
that he takes out any one of them.  
Since there is only one black ball,  
Let B be the event that we get a black ball  
The number of favourable outcomes = 1 
The number of possible outcomes = 3 
P(B)=  
The number of favourable outcomes
The number of possible outcomes
 
1
P(B) =  
3
 
 
2)  Suppose, we throw a die once,  
(i) What is the probability that we get a number greater than 3  
(ii) What is the probability of getting a number less than  or equal to 3? 
Solution: 
 Let E be an event that we get a number greater than 3.  
 The possibilities according to given condition are 4, 5, 6.  
 The total possibilities are 1, 2, 3,4,5,6.  
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
 
 Let D be the event that we get a number less than or equal to 3. 
 The given possibilities are 1, 2, 3.  
 The total possibilities are 1, 2, 3, 4, 5, 6.  
Probability 
 
 
 
The number of favourable outcomes = 3 
The number of possible outcomes = 6 
P(E) = 
The number of favourable outcomes
The number of possible outcomes
 
        = 
3
6
 
 
1
P(E) =  
2
   
 
3) A single card is drawn from a well shuffled pack of 52 cards.  
 Calculate the probability that the card is 
 (i)  a King 
 (ii) not a king 
Solution:  
(i) Let E be the event that the card is a King.  
 There are 4 kings in a deck  
 The number of favourable outcomes = 4 
 The number of possible outcomes = 52 
 P (E) = 
The number of favourable outcomes
The number of possible outcomes
 
         =  
4
52
 
 
1
P(E) =  
13
 
(ii) Let D be the event that the card is not a king  
 Hence D =  E  
 Therefore,  
 P( E )  = 1- P(E) 
   = 1- 
1
13
 
 P( E ) =  
12
13
      
12
P(D) =  
13
 
Probability 
 
4)  Two players, Rahul and Rohit are playing a Badminton match.   
The probability of Rahul winning the match is 0.37.  
What is the probability of  Rohit winning the match? 
Solution: 
 Let E denote the event that Rahul wins the match and  
 D denote the event that Rohit wins the match. 
 Given that, 
 Probability that Rahul wins the match = P(E) = 0.37 
 Therefore 
 Probability that Rohit wins the match  = P(D) = 1- P(E) 
 Probability that Rohit wins the match  = P(D) = 1- 0.37 = 0.63  
 
 
5) There are 60 students in class XII of a school of whom 35 are boys.  
 The class teacher has to select a class monitor. She tell the students to write 
 their names on an identical piece of paper.  Then she put all the chits in a  
 bowl and stirs it thoroughly and draws a card at random from the bowl.  
 What is the probability that the name written on the chit is that of  
 (i) a girl (ii) a boy? 
Solution: 
 The number of possible outcomes = 60 
 (i)  
 Let G be the event that the name drawn is that of a girl  
 The number of favourable outcomes = 25 
 P(G) = 
The number of favourable outcomes
The number of possible outcomes 
 
 P(G) = 
25
60
= 
5
12
 
  
5
P(G) =
12
 
  (ii) 
 Let B be the event that the name drawn is that of a boy  
 P(B) = 1 – P(G) 
Probability 
 
  
 
P(B) = 1 - 
5
12
 
7
P(B) =
12
 
5) A bas contains only yellow marbles. Avinash takes one marble without looking  
 into the bag. What is the probability that he takes out  
 (i) a pink marble (ii) a black marble 
Solution: 
 (i)  
 Let P be the event that a pink marble is taken out 
 Since the bag contains no pink marbles 
 The number of favourable outcomes = 0 
 P (P) = 
The number of favourable outcomes
The number of possible outcomes 
 
 P(P) =0  
 (ii) 
 Let Y be the event that a black marble is taken out 
 Since the bag only contains yellow marbles & no black marble. 
    ( )   
 
6) A box contains 8 green marbles, 3 white marbles and 9 orange marbles.  
 One marble is taken out of the box at random. What is the probability that 
 the marble taken out will be  (i) green   (ii) not white   (iii) orange.  
Solution:  
 The number of possible outcomes = 20 
 (i)  
  Let G be the event that a green marble is taken out.  
  The number of favourable outcomes = 8 
  P (G) = 
The number of favourable outcomes
The number of possible outcomes 
 
  P (G) = 
8
20
 
Probability 
 
 
 
  
2
P(G) =
5
 
 (ii)   
  Let E be the event that a marble is taken out which is not white  
  i.e it can be green or orange 
  The number of favourable outcomes for green & orange marbles = 17 
  P(E) = 
The number of favourable outcomes
The number of possible outcomes 
 
  P(E) = 
17
20
 
  
17
P(E) =
20
 
 (iii) 
   Let O be the event that an orange marble is taken out.  
  The number of favourable outcomes = 9 
  P (O) = 
The number of favourable outcomes
The number of possible outcomes 
 
   
   
9
P(O) =
20
  
 
7) A bag contains 16 candies out of which x are orange flavoured 
 (i) If one candy is drawn at random, what is the probability that it will be  
 Orange flavoured. 
 (ii) If 8 more orange flavoured candies are added to the bag, the probability of  
 taking out an orange flavoured candy is doubled than that in (i). Find x.  
Solution: 
 (i) 
  The number of possible outcomes = 16 
  Let O be the event that the candy taken out is orange flavoured 
  The number of favourable outcomes = x 
    
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