Chapter 15. Probability

Class 10 Maths Chapter 14. Probability Multiple Choice Questions And Solution :

Question : The probability of getting a number 8 in a single throw of a die : [SEBA 2023]

(a)       (b)      (c)  1    (d)  0

Solution : (d) 0

[ Total number of possible out of a dice = 6

Since no face of the is marked 8 , so there is no outcomes favourable to 8 , i.e., the number of outcomes is 0 .

P( getting 8) ]

Question : What is the probability of getting a number 9 in a single throw of a die ? [SEBA 2021]

(a)     (b) 1    (c)      (d)  0

Solution :  (d) 0

[  There are 6 surfaces on a dice .

Total number  of possible out of a dice = 6

Since no face of the is marked 9 , so there is no outcomes favourable to 9 , i.e., the number of outcomes is 0 .

P( getting 9 ) ]

Question : The sum of the probabilities of all the elementary events of an experiment is : [SEBA 2020]

 (a) 1       (b)  1.25       (c) 1.4        (d) 2

Solution :   (a)  1

[ The sum of the probabilities of all the elementary events of an experiment is 1 .]  

Question : The probability of an impossible event is :  [SEBA 2019]

(a)  0       (b) 0.25      (c) 0.5    (d)  1

Solution :  (a)  0

[The probability of an impossible events is 0 .]

Question : The probability of an event ‘E’ + the probability of the event ‘not E’ is : [SEBA 2018]

(a) 2        (b)  1        (c)  0       (d)  0.1 

Solution :  (b)  1

[ We know that ,  ]

Q2. Which one of the following is the probability of an event ?      [SEBA 2017]

 (a)           (b)          (c)   – 1.5         (d)  1.001

Solution :  (a)   

[ The probability of an even E is a number P(E) such that  ]

Q7. A number is selected from the first 100 natural numbers . The probability  that the number  is divisible by 7 is :   [SEBA 2016]

 (a)           (b)             (c)           (d) 

Solution : (a)   

[  Total number of natural numbers = 100

The number is divisible by 7 = 14

{7,14,21,28,35,42,49,56,63,70,77,84,91,98}

P(getting a number divisible by 7)    ]

Question : A die is thrown once , the probability of getting a prime number is : [SEBA 2015]

(a)          (b)         (c)         (d)   

Solution :  (c)

[ Total number of possible outcome = 6

The number of a prime number = 3  (2 , 3 , 5)

P(getting a prime number)   ]

Question :  If for any event E, P(E) = 0.11 , when  means ‘‘ an event not happening E ’’ then the value of  is : [ SEBA 2014]

 (a)  1.00    (b) 9.99   (c) 0.89  (d) 1.11

Solution : (c) 0.89

[ We have,  

 

    ]

Question : Which of the following number can the probability of an event ?  [SEBA 2013]

(a)  – 0.8    (b)     (c)    (d) 1.45

Solution :  (b)

[ Since,  . Because ,   ]

Question : The probability of a sure event (or certain event) is : 

(a)  0       (b) 25 %      (c) 1.5    (d)  1

Solution :  (a)  0

[The probability of a sure event or certain event is 1 .]

Question :  If two different dice are rolled together, the probability of getting an even number on both dice is : [2014 Dehli]

  (a)           (b)        (c)         (d)                 

Solution :  (d)     

[  Total number of possible outcomes = 36

The number of favourable to the event = 9

P(getting an even number on both dice) ]

Question :  Two different coins are tossed simultaneously . The probability of getting at least one head is :[CBSE 2014F]

 (a)         (b)          (c)         (d)                                  

Solution :  (c)       [ P(getting at least one head)   { HH , HT , TH } ]

Question : A bag contain 8 red , 6 white and 4 black balls . A ball is drawn at random from the bag.Then the probability that the drawn ball  getting neither white nor black is :

   (a)            (b)             (c)            (d) 

Solution :  (b)    

[  Total number of balls = 8 + 6 + 4 = 18

The number of balls neither white nor black = 8

  P(getting neither white nor black)    ]

Question :  The probability that a number selected at random from the numbers 1 , 2 , 3 , ……, 15 is a multiple of 4 is : [CBSE 2014]

 (a)       (b)        (c)        (d) 

Solution :  (c) 

[ P(getting a multiple of 4)    {4 , 8 , 12} ]

Question :   Which of the following cannot be the probability of an event ?

 (a)          (b)        (c) 15  %  (d) 0.7 

Solution:  (b)                 

Question :  In a family of 3 children, the probability of having at least one boy is :  [ CBSE 2014]

 (a)       (b)         (c)          (d) 

Solution :   (d)      

[ Total number of possible outcome

 The number of at least one boy  

      ]

Class 10 Probability Filled in the blanks :

Q1.  Probability of an event   + Probability of the event ‘ not  ’  .

Solution :  1   [  Since,    ]

Q2. A die is thrown once , then the probability of getting a number greater than 4 is  .

Solution :     

[ P(getting a number greater than 4)     {5 , 6}     ]

Question : The probability of an event  is a number  such that   .

Solution :    .

Q4. One card is drawn from a well-shuffled deck of 52 cards , then the probability of getting  a spade is   .  [SEBA 2018]

Solution : 

[  P(getting a spade)    ]

Question : The probability of an impossible event is  . (1 / 5 / 0 / 6)   [SEBA 2023]

Solution : The probability of an impossible event is  .

Question : A die is thrown once . The probability of getting a number less than 5 is  .     [SEBA 2023]

Solution : The probability of getting a number less than 5 is  .

Question : The probability that it will rain tomorrow is 0.85 , then the probability that it will not rain tomorrow is  .

Solution :  0.15   [ We have ,    ] 

Question : The sum of the probabilities of all the elementary events of an experiment is   .

Solution:  1

Question : The probability of an event that is certain to happen is  0 . Such an event is called   .

Solution:  Impossible event .

Question : For any event  ,  , Where  stands for ‘not  ’.  and  are  called  events .

Solution:  Complementary .

Question : Two players , Sangeeta and Reshma , play a tennis match . It is known that the probability of Sangeeeta winning the match is 0.62 . Then the probability of Reshma winning the match is   .

Solution:   0.38 

[ The probability of Reshma’s winning      ]

Question :  The probability of an event is greater than or equal to    and less than or equal to  .

Solution:  0   and 1 

Class 10 Probability  Answers following the questions

Question :  A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and these are equally likely outcomes . Find the probability that the arrow will point  at any factor of 8 .   [2015F]

Solution:   The total number of possible outcome  

The number of factor of 8   

P(getting a factor of 8)

Question :  If three different coins are tossed together, then find the probability of getting two heads . [2017C]

Solution : Total number of elementary events   

The favourable number of elementary events  

    P(getting two heads)

Question : One card is drawn from a well-shuffled deck of 52 cards . Find the probability of getting a spade . [SEBA 2018]

Solution:  Total number of  possible outcome   

 The number of a spade  .

 P(getting a spade)

Question : Cards marked with number 3 , 4 , 5 , ……… , 50 are placed in a box and mixed thoroughly . A card is drawn at random from the box . Find the probability that the selected card bears a perfect square number .  [2016 Delhi]

Solution :  Total number of elementary events  .

 The favourable number of elementary events      [ 1 , 4 , 9 , 16 , 25 , 36 , 49]

  P(getting a perfect square number)  

Question :  Find the probability of getting the letter M in the word ‘‘ MATHEMATICS ’’ .

Solution : Total number of elementary events  .

 The favourable number of elementary events   

  P(getting the letter M)      

Question :   A letter is chosen at random from the letter of the word ‘‘ PROBABILITY ’’ . Find the probability that it is not a vowel .

Solution:  The total number of word  

The number of  ‘‘ not a vowel ’’  

  

Question :  A bag contains 3 red and 5 black balls . A ball is drawn at random from the bag . What is the probability that the drawn ball is not red ?  [2017C Delhi]

Solution:  Total number of balls  

  

Question :   What is the probability of getting a number less than 7 in a single throw of a die ?

 Solution:   Total number of possible outcome  

 

Question :  Gopi buys a fish from a shop for his aquarium . The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish . What is the probability that the fish taken out is a male fish ?

Solution: Total number of fishes  

   

Question :  It is given that a group of 3 students, the probability of 2 students not having the same birthday is 0.992 . What is the probability that the 2 students have the same birthday .

Solution :  2 students from a groups of 3 students not having the same birthday  

    2 students from a group of 3 students having the same birthday  

    

Question :  A card is drawn at random from a well shuffled pack of 52 playing cards . Find the probability of getting neither a red card nor a queen .  [CBSE 2016]

Solution : Total number of elementary events  .

The favourable number of elementary events  .    

 P(getting neither a red nor a queen)  

Class 10 Probability 2 Marks Questions and Answers 

SECTION = B [2 Marks]

Question : A bag contains 5 white , 6 red and 4 green marbles . One marble is drawn at random from the bag .What the probability that the marble drawn is not red ?  [SEBA 2013]

Solution :  Total number of marbles = 5 + 6 + 4 = 15

The number of marbles is ‘not red’ = 5 + 4 = 9

 P(not red)  

Question :  Five cards – the ten , jack , queen , king and ace of diamonds , are well-shuffled with their face downwards . One card is then picked up at random .

  (i) What is the probability that the card is the queen ?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is  (a) an ace ? (b) a queen ?

Solution: Total number of possible outcome  

(i) The number of favourable outcome  

P(getting the queen)  

(ii) Total number of possible outcome   [Queen out]

(a)  P(getting an ace)

(b) P(getting a queen)

Question : 12 defective pens are accidentally mixed with 132 good ones . It is not possible to just look at a pen and tell whether or not it is defective . One pen is taken out at random from this lot . Determine the probability that the pen taken out is a good one .

Solution : Total number of pen

The number of good pen  .

P(getting the pen taken out is a good one)

Question : A lot consists of 144 ball pens of which 20 are defective and the others are good . Nuri will buy a pen if it is good, but will not buy if it is defective . The shopkeeper draws one pen at random and gives it to her . What is the probability that  (i) She will buy it ? (ii) She will not buy it ? [SEBA 2016]

Solution:  Total number of ball pens = 144 .  

The number of defective ball pens = 20 .

The number of good ball pens = 144 – 20 =124 

(i) P( getting a good ball pens)   .

(ii) P(getting a defective ball pens)

Question :  A bag contains 3 red balls and 5 black balls . A ball is drawn at random from the bag . What is the probability that the ball drawn is :   (i) red ? (ii) not red ?  [SEBA 2019]

Solution : Total number of balls  = 3 + 5 = 8

(i) The number of red balls  = 3    .  

 P( getting red balls)    

(ii) The number of balls are not red = 8 – 3 = 5 . 

 P(getting not red balls)             

Question : Hari tosses two different coins simultaneously (say, one is of Rs 1 and other of Rs 2). What is the probability that she gets at least one head? [SEBA 2023]

Solution : The sample space = {(H, H), (H, T), (T, H), (T, T)}

Total number of the possible outcomes = 4  

The number outcomes favourable to the event ‘at least one head’  = 3  [ (H, H), (H, T) and (T, H) ]

 P(getting at least one head)

Question : A bag contains  3 red balls and 5 black balls . A ball is drawn at random from the bag . What is the probability that the ball drawn is  (i) red   (ii) not red [SEBA 2019]

Solution : Total number of balls  = 3 + 5 = 8

(i)  P(getting the red balls)         

(ii)  P(getting not red balls)  

Question : Two different dice are rolled simultaneously . Find the probability that the sum of numbers appearing on the two dice is 10 .  [2014F]

Solution : Total number of possible outcome  = 36 

The favourable number of elementary events  = 3   [ (4 , 6) , (5 , 5) , (6 , 4) ]

 P(getting the sum of numbers appearing on the two dice is 10)   

Question : A die is thrown once . Find the probability of getting :  (i)  a prime number    (ii)  a number lying between 2 and 6 .[SEBA 2017]

Solution :  Total number of possible outcome  = 6 

(i)   The favourable number of elementary events  = 3  [ 2 , 3 , 5 ]

P(getting a prime number)    

(ii)   The favourable number of elementary events  = 3  [3 , 4 , 5 ]

 P(getting a number lying between 2 and 6)   

Question : One card is drawn from a well-shuffled deck of 52 cards . Find the probability of getting .(i)  a king of red colour    (ii) a spade   (iii) a red face card  [SEBA 2020]

Solution : Total number of possible outcome  = 52 

  (i)   The favourable number of elementary events  =  2  [Hearts and diamonds are of red colour]

P(getting a king of red colour)   

 (ii) The favourable number of elementary events  =  13   [13 card of the spade]

 P(getting a spade)   

 (iii)  The favourable number of elementary events  =  6    [2Kings , 2Queens  and 2 jacks]

   P(getting a spade)    

Question : A bag contains 5 white , 6 red and 4 green marbles . One marble is drawn at random from the bag .What the probability that the marble drawn is not red ?    [SEBA 2013]

Solution : Total number of marbles

 P(not  red marbles)  

Question :  A bag contains a red ball , a blue ball and a yellow ball, all the balls being of the same size .Kritika takes out a ball from the bag  without looking into it . What is the probability that she takes out the –

 (i) yellow ball ?    (ii) red ball  ?    (iii) blue ball ?

Solution : Total number of balls

 (i) P(getting yellow ball)    

 (ii) P(getting red ball)   

(iii) P(getting blue ball)  

Question : Two different dice are tossed together . Find the probability  of getting : (i)   same number on both dice (i.e. a doublet) . (ii)  a multiple of 3 as the sum . [CBSE 2014]

Solution :  Total number of possible outcome  .

 (i) The total number of elementary events = 6 [(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)]

P(getting the number on each die is even)   

 (ii) The total number of elementary events  =  12 . [(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3),(6,6)]

 P(getting a multiple of 3 as the sum)  

Question : From all the two digit numbers, a number is chosen at random . Find the probability that the chosen number is a multiple of 7 .   [CBSE 2017C]

Solution :  The total number of possible outcome

  The favourable number of elementary events 

  P(getting the number is a multiple of 7)                

Question : A bag contains 25 cards numbered from 1 to 25 . A card is drawn at random from the bag . Find the probability that the number on the drawn card is : (i)  divisible by 3 or 5 . (ii)  a perfect square number . [2015 DELHI]

Solution :  The total number of the cards = 25  .

 (i)  The favourable number of elementary events  

 P( getting the number divisible by 3 or 5)   

 (ii) The favourable number of elementary events 

  P(getting a perfect square number)   

 Class 10 Probability 3 Marks Questions and Answers 

SECTION = C [3 Marks]

Question :  A game of chance consists of spinning  an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , which are equally likely outcomes. What is the probability that the arrow will point at : (i) an odd number   (ii)  a number greater than 3   (iii) a number less than 9 .    [2016 Delhi]

       

Solution :  The total number of possible outcome = 8   [1,2,3,4,5,6,7,8]

 (i)  The total number of an odd number = 4    [1,3,5,7]

 P(getting a odd number)  

 (ii)  The total number of a number greater than 3 = 5    [4,5,6,7,8]

P(getting a number greater than 3)  

(iii)   The total number of a number less than 9 = 8

 P(getting a number less than 9)

Question :  All red face cards are removed from a pack of playing cards . The remaining cards were well shuffled and then a card is drawn at random from them . Find the probability that the drawn cards is : (i) a red card  (ii) a face card    (iii) a card of clubs  [2015 Delhi]

Solution : Total number of possible outcome  

         [ 6 red face card are removed from the pack]

(i) The total number of a red card   

  P(getting a red card)  

(ii)  The total number of a face card  =   

  P(getting a face card)  

 (iii) The total number of a card of clubs  

 P(getting a card of clubs)    

Question : Three different coins are tossed together .Find the probability of getting : (i) exactly two heads   (ii) at least two heads [CBSE 2016]        

Solution : Total number of possible outcome    [ HHH,HHT,HTH,THH,HTT,THT,TTH,TTT  ]

(i) The favourable number of elementary events  

 P(getting the exactly two heads)  

(ii) The favourable number of elementary events 

 P(getting at least two heads)

Question :  Cards numbered 1 to 30 are put in a bag . A card is drawn at random from this bag . Find the probability that the number on the drawn card is :  (i) not divisible by 3 . (ii) a prime number greater than 7 .  (iii) not a perfect square number . [CBSE 2014 F]

Solution : Total number of possible outcome  .

(i) The favourable number of elementary events  

P(not divisible by 3)    

(ii) The favourable number of elementary events 

 P(getting a prime number greater than 7)  

 (iii)  The favourable number of elementary events 

 P(not a perfect square number)  

Question :  A piggy bank contains hundred 50 p coins , fifty Rs. 1 coins , twenty Rs. 2 coins and ten Rs. 5 coins . If it is equally likely that one of the coins will fall out when the bank is turned upside down , what is the probability that the coin (i) will be a 50 p coin ?  (ii) will not be a Rs. 5 coin ?

Solution : Total number of  coins = 100+50+20+10 = 180 

(i)  The total number of a 50 p coins = 100  .

 P(getting a 50 p coin)  

(ii) The total number of a Rs. 5 coins   

 P(getting a Rs. 5 coin)  

Question :   A number  is selected at random from the numbers 1 , 2 , 3 and 4 . Another number  is selected at random from the numbers  1 , 4 , 9 and 16 . Find the probability that product of  and  is less than 16 .  [CBSE 2016]

Solution :  The total number of possible outcome = 16  .[1×1, 1×2, 1×3, 1×4, 2×1, 2×4, 2×9, 2×16, 3×1, 3×4, 3×9, 3×16, 4×1, 4×4, 4×9, 4×16]

The total number of elementary events  =  8  [1×1, 1×4, 1×9, 2×1, 2×4, 3×1, 3×4, 4×1]

P(getting the product of  and  is less than 16)            

Question :   A box contains cards, number from 1 to 90 . A card is drawn at random from the box. Find the probability that the selected card bears : (i)  a perfect square number   (ii)  a prime number between 8 to 40 .

Solution :  Total number of possible  outcome  .

(i) The total number of a perfect square number  from 1 to 90 = 9 [1,4,9,16,25,36,49,64,81]

P(getting a perfect square number)  

(ii) The total number of a prime number between 8 to 40 = 8  [11,13,17,19,23,29,31,37]

 P(getting a prime number between 8 to 40)    

Question :  Five cards – the ten , jack , queen , king and ace of diamonds , are well-shuffled with their face downwards . One card is then picked up at random . (i) What is the probability that the card is the queen ?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace ?    (b) a queen ?

Solution :  The total number of possible outcome = 5    [ten, jack ,queen, king  and ace]

 (i) The number of elementary events  = 1   [ Queen only]

   P( getting the queen)  

 (ii)  The total number of elementary events  = 4  [ The queen has removed]

  (a) P(getting an ace)      

   (b)  P(getting a queen)

Question :  A box contains cards bearing numbers from 6 to 70 . If one card is drawn at random from the box ,find the probability that it bears : (i) a one digit number.   (ii) a number divisible by 5 , (iii) an odd number less than 30   (iv) a composite number between 50 and 70 . [CBSE 2015 F]

Solution :  Total number of possible outcome  

 (i) Total number of a one digit number    [6 , 7 , 8 , 9]

 P(getting a one digit number)  

(ii)  Total number of a number divisible by 5    [10,15,20,25,30,35,40,45,50,55,60,65,70]

P(getting a number divisible by 5)   

(iii)  Total number of an odd number less than 30  [7,9,11,13,15,17,19,21,23,25,27,29]

 P(getting an odd number less than 30)    .

(iv) Total number of  a composite number between 50 and 70   [ Composite number between 50 and 70 are 51,52,54,56,57,58,60,62,63,64,65,68,69,70]

 P(getting a composite number between 50 and 70)