Read and download free pdf of CBSE Class 10 Maths Probabilty Worksheet. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 15 Probability Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

## Chapter 15 Probability Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

### Class 10 Mathematics Chapter 15 Probability Worksheet Pdf

**VERY SHORT ANSWER TYPE QUESTIONS :**

**VERY SHORT ANSWER TYPE QUESTIONS :**

**Question. From a well-shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen. **

**Answer :** ∵ Total number of cards = 52

Since, the number of black queens = 2

∴ Number of favourable outcomes = 2

⇒ P(E) = 2/52 = 1/26.

**Question. Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. What is the probability that the number on the card taken out is an even number? **

**Answer :** Total number of cards (3 to 20) = 18

∴ Number of possible outcomes = 18

Since cards having even numbers (4, 6, 8, 10, 12, 14, 16, 18 and 20) are 9,

∴ Number of favourable outcomes = 9

∴ P(E) = 9/18 or 1/2.

**Question. Cards each marked with one of the numbers 6, 7, 8, ....., 15 and placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting a card with number less than 10? **

**Answer :** ∵ There are 10 cards.

∴ Total number of possible outcomes = 10

Cards marked with a number less than 10 are: 6, 7, 8 and 9

i.e. The number of favourable outcomes = 4

∴ P(E) = 4/10 or 2/5.

**Question. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. Find the probability of getting a black ball. **

**Answer :** Total number of balls = 4 + 6 = 10

⇒ All possible outcomes = 10

Since, number of black balls = 6

∴ Number of favourable outcomes = 6

⇒ P(E) = 6/10 or 3/5 .

**Question. Find the probability that a number selected from the numbers 1 to 25 which is not a prime number when each of the given number is equally likely to be selected.**

**Answer :** Total number of given numbers = 25

Since the numbers 2, 3, 5, 7, 11, 13, 17, 19 and 23 are prime number.

There are 9 numbers.

∴ Number of numbers that are not prime = 25 − 9 = 16

∴ Number of favourable outcomes = 16

⇒ Required probability = 16/25.

**Question. What is the probability that two different friends have different birthdays? (Ignoring leap year).**

**Answer :** Number of days in a year = 365

⇒ Number of possible outcomes = 365

Since they have different birthdays.

∴ Number of favourable outcomes = 365 − 1 = 364

∴ P(E) = 364/365.

**Question. A letter is chosen at random from English alphabet. Find the probability that the letter chosen precedes ‘g’.**

**Answer :** Total number of letters in English alphabet is 26.

∴ Total number of possible outcomes = 26

∵ Letters preceding ‘g’ are:

a, b, c, d, e and f

∴ Favourable outcomes = 6

⇒ Required probability = 6/26 = 3/13.

**Question. A die is thrown once. Find the probability of getting an odd number.**

**Answer :** Total number of possible outcomes = 6 [∵ Numbers 1 to 6 are marked on the faces of a die]

∵ odd numbers are 1, 3 and 5

∴ Favourable outcomes = 3

∴ Required probability = 3/6 = 1/2.

**Question. A box contains cards marked with numbers 5 to 20. A card is drawn from the bag at random. Find the probability of getting a number which is a perfact square. **

**Answer :** ∵ Total number of cards = 16

∴ Possible outcomes are 16.

Since the numbers 9 and 16 are perfect numbers,

⇒ Number of favourable outcomes = 2

∴ P (E) = 2/16 or 1/8.

**Question. A bag contains 9 black and 12 white balls. One ball is drawn at random. What is the probability that the ball drawn is black?**

**Answer :** Total number of balls = 9 + 12 = 21

⇒ Number of possible outcomes = 21

Number of black balls = 9

⇒ Number of favourable outcomes = 9

∴ Required probability = 9/21 = 3/7.

**Question. A die is thrown once. Find the probability of getting a number less than 3.**

**Answer :** Numbers on the faces are 1, 2, 3, 4, 5 and 6.

∴ Number of possible outcomes = 6

Numbers less than 3 are 1 and 2.

⇒ Number of favourable outcomes = 2

∴ P(E) = 2/6 or 1/3.

**Question. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of getting a black king? **

**Answer :** ∵ Total number of cards = 52

∴ Number of possible outcomes = 52

Number of black king = 2

∴ P(Black king) = 2/52 = 1/26.

**Question. A die is thrown once. Find the probability of getting a number greater than 5. **

**Answer :** Total number of possible outcomes = 6

Since only one number i.e., 6 is greater than 5

∴ Favourable number of outcomes = 1

⇒ P(E) = 1/6.

**Question. A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will not be a white marble?**

**Answer : **Total number of balls = 3 + 2 + 4 = 9

∴ Number of possible outcomes = 9

Since, number of white balls = 2

∴ Number of balls which are not white

= 9 − 2 = 7

⇒ Number of favourable outcomes = 7

∴ P(E) = 7/9.

**Question. Two friends were born in the year 2000. What is the probability that they have the same birthday ?**

**Answer :** Since the year 2000 was a leap year,

∴ Total number of days in the year = 366

∵ They have the same birthday.

∴ Number of favourable outcomes = 1

⇒ P(E) = 1/366.

**Question. A letter of English alphabet is chosen at random. Determine the probability that the letter is a consonant. **

**Answer :** There are 26 letters in English alphabets.

⇒ Possible outcomes = 26

Q There are 5 vowels (a, e, i, o, u) and remaining are consonants.

∴ Number of consonants = 26 – 5 = 21

⇒ Favourable outcomes = 21

∴ P(consonants) = 21/26

**Question. Find the probability of obtaining 7 on a single toss of one die.**

**Answer :** Numbers marked on a die are:

1 , 2 , 3 , 4 , 5 , 6

∴ There are six different possible outcomes.

But none of these outcomes would produce a 7.

⇒ Favouable outcome = 0

∴ P_{(7)} = 0/6 = 0

When an event cannot possibly succeed, we say it is an impossible event and probability of an impossible event is zero.

i.e. P_{(impossible event)} = 0

**SHORT ANSWER TYPE QUESTIONS :**

**SHORT ANSWER TYPE QUESTIONS :**

**Question. Two dice are thrown at the same time and the product of numbers appearing on them is noted.**

**Find the probability that the product is less than 9.**

**Answer :** Total number of possible outcomes = 6 × 6 = 36

∵ The outcomes such that the product of numbers appearing on the faces is less than 9 are:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (4, 1),

(4, 2), (5, 1) and (6, 1).

∴ Number of favourable outcomes = 16

⇒ Required probability = 16/36 = 4/9.

**Question. The king, queen and jack of diamonds are removed from a pack of 52 cards are then the pack is well-shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of**

**(i) diamonds**

**(ii) a Jack**

**Answer :** ∵ There are 52 card in the pack.

And number of cards removed = 3 [1 king + 1 queen + 1 jack = 3 cards]

∴ Remaining cards = 52 − 3 = 49

∴ (i) P_{(a diamond)} = 13 − 3/49 = 10/49 [∵ Total diamonds are 13]

(ii) P(a jack) = 4 − 1/49 = 3/49 [∵ Total jacks are 4]

**Question. Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the taken out card is:**

**(i) a prime number less than 10.**

**(ii) a number which is a perfect square**.

**Answer : **Numbers from 5 to 50 are 46.

∴ Total number of possible outcomes = 46.

(i) Prime numbers (less than 10) are 5, 7.

∴ Favourable outcomes = 2

⇒ P_{(prime number less than 10)} = 2/46 = 1/23

(ii) Perfect square are 9, 16, 25, 36 and 49

∴ Number of favourable outcomes = 5

⇒ P_{(perfect square)} = 5/46.

**Question. An integer is chosen between 0 and 100. What is the probability that it is divisible by 7?**

**Answer :** ∵ Numbers between 0 and 100 are 99.

∴ Total possible outcomes = 99

Since following numbers are divisible by 7 :

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91 and 98.

∴ Favourable outcomes = 14

⇒ Required probability = 14/99.

**Question. In a game of chance there is spinning of an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and there are equally likely outcomes. What is the probability that it will point at**

**(i) 7? **

**(ii) an odd number?**

**(iii) a number less than 9?**

**Answer :** Since, following numbers are marked on the disc:

1, 2, 3, 4, 5, 6, 7, 8

(iii) Q The numbers less than 9 on the disc are:

1, 2, 3, 4, 5, 6, 7, 8, (i.e. 8 outcomes)

∴ Favourable outcomes = 8

⇒ P_{(number less than 9)} = 8/8 = 8

**Question. Find the probability that a number selected at random from numbers 3, 4, 5, ....., 25 is prime.**

**Answer :** Total numbers are 23.

∴ Number of possible outcomes = 23

Since, prime numbers are 3, 5, 7, 11, 13, 17, 19 and 23.

∴ Number of favourable outcomes = 8

⇒ P (E) = 8/23.

**Question. A die is thrown once. Find the probability of getting:**

**(i) an even prime number.**

**(ii) a multiple of 3. **

**Answer :** Total numbers on the faces of a die are 1, 2, 3, 4, 5 and 6

⇒ Number of favourable outcomes = 6

(i) Even prime number is only one i.e. 2

∴ Favourable outcome = 1

⇒ P_{(even prime number)} = 1/6

(ii) Multiples of 3 are 3 and 6

∴ Favourable outcomes are 2.

⇒ P_{(multiple of 3)} = 2/6 = 1/3.

**Question. From a group of 2 boys and 3 girls, two children are selected at random. Find the probability such that at least one boy is selected.**

**Answer :** Let B_{1} and B_{2} be two boys and G_{1}, G_{2} and G_{3} be the three girls

Since two children are selected at random,

∴ Following are the possible groups:

B_{1}B_{2}, B_{1}G_{1}, B_{1}G_{2}, B_{1}G_{3}, B_{2}G_{1}, B_{2}G_{2}, B_{2}G_{3}, G_{1}G_{2}, G_{1}G_{3}, G_{2}G_{3}

∴ Total number of possible outcomes = 10

Since, one boy is to be selected,

∴ Favourable outcomes are:

B_{1}B_{2}, B_{1}G_{1}, B_{1}G_{2}, B_{1}G_{3}, B_{2}G_{1}, B_{2}G_{2} and B_{2}G_{3}.

⇒ Number of favourable outcomes = 7

∴ Required probability = 7/10.

**Question. A bag contains 4 red, 5 black and 3 yellow balls. A ball is taken out of the bag at random. Find that the ball taken out is of:**

**(i) yellow colour**

**(ii) not of red colour. **

**Answer :** Total number of balls = 4 + 5 + 3 = 12

⇒ Total number of possible outcomes = 12

(i) ∵ Number of yellow balls = 3

∴ Number of favourable outcomes = 3

⇒ P_{(yellow)} = 3/12 = 1/4

(ii) Number of balls that are not red = 12 − 4 = 8 [∵ There are 4 red balls]

∴ Favourable outcomes = 8

⇒ P_{(not red)} = 8/12 = 2/3.

**Question. A bag contains 7 red, 5 white and 3 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is neither white nor black.**

**Answer :** Total number of balls

= 7 + 5 + 3

= 15

∵ Number of white balls = 5

Number of black balls = 3

∴ Number of balls that are neither white nor black = 15 − [5 + 3]

= 15 − 8

= 7

∴ Required probability = 7/15.

**Question. Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has a square number. **

**Answer :** Number of numbers between 2 to 101 are 100

∴ Total number of possible outcomes = 100

Since, the perfect numbers between 2 and 101 are:

4, 9, 16, 25, 36, 49, 64, 81 and 100

∴ Number of favourable outcomes = 9

⇒ Required probability = 9/100.

**Question. A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability of this ball being not a blue ball.**

**Answer :** Total number of balls = 10 + 5 + 7 = 22

∴ Number of possible outcomes = 22

Since there are 5 blue balls.

∴ Number of balls which are not blue

= 22 − 5 = 17

∴ Favourable outcomes = 17

⇒ Required probability = 17/22.

**Question. A box contains 20 cards, numbered from 1 to 20. A card is drawn from the box at random. Find the probability that the number on the drawn card is:**

**(i) even **

**(ii) multiple of 3.**

**Answer :** Total numbers from 1 to 20 are 20

∴ Number of possible events = 20

(i) Even numbers are:

2, 4, 6, 8, 10, 12, 14, 16, 18 and 20

∴ Number of favourable outcomes = 10

⇒ Probability of getting an even number = 10/20 = 1/2

(ii) Since, multiples of 3 are:

3, 6, 9, 12, 15 and 18

∴ Number of favourable outcomes = 6

⇒ Probability of getting a multiple of 3

= 6/20 = 3/10.

**Question. Two dice are thrown simultaneously. What is the probability that**

**(i) 5 will not come up on either of them?**

**(ii) 5 will come up on at least one?**

**(iii) 5 will come up at both dice?**

**Answer :** ∵ The two dice are thrown simultaneously

∴ Possible outcomes are = 6 × 6 = 36

(i) When 5 will not come up on either of them:

Favourable outcomes are: 36 − 11 = 25

∴ P_{(5 will not come up on either dice)} = 25/36

(ii) When 5 will come on at least one dice:

Favourable outcomes are: 36 − 25 = 11

∴ P_{(5 will come on at least one dice)} = 11/36

(iii) When 5 will come up on either dice:

Favourable outcome is only one i.e. (5, 5)

∴ P_{(5 on both dice)} = 1/36.

**Question. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing a**

**(i) face card**

**(ii) card which is neither a king nor a red card. **

**Answer :** Total number of cards = 52

(i) Total number of face cards = 12 [4 Jacks + 4 Queens + 4 Kings]

∴ Number of favourable outcomes = 12

⇒ P_{(face)} = 12/52 = 3/13

(ii) Number of kings = 4

Number of red cards = 13 + 13 = 26

∴ Number of cards that are neither a red nor a king = 52 − 4 − 26 + 2 (red kings)

= 24

⇒ Favourable outcomes = 24

∴ P_{(neither king nor red)} = 24/52 = 6/13

**Question. Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 9. **

**Answer :** Following are the possible outcomes for two dice thrown simultaneously:

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

∴ Total number of possible outcomes = 36

Following outcomes have a sum of more than 9:

(4, 6), (6, 4), (5, 5), (5, 6), (6, 5) and (6, 6)

i.e. Favourable outcomes = 6

∴ The required probability = 6/36 or 1/6.

**Question. In a bag-X, there are four cards numbered 1, 3, 5 and 7 respectively. In an another bag-Y, there are three cards numbered 2, 4 and 6 respectively. A card is drawn at random from each bag.**

**(a) Write all the possible outcomes.**

**(b) Find the probability that the sum of these two cards drawn is:**

**(i) 7 **

**(ii) even**

**(iii) more than 7**

**Answer :** (a) There are 12 possible outcomes

**Question. A die is thrown once. Find the probability of getting:**

**(i) a prime number**

**(ii) a number divisible by 2. **

**Answer :** ∵ The numbers on the faces of a die are 1, 2, 3, 4, 5 and 6.

∴ Number of possible outcomes = 6

(i) Prime numbers are 2, 3 and 5

∴ Number of prime numbers = 3

⇒ Number of favourable outcomes = 3

∴ P_{(prime number)} = 3/6 = 1/2

(ii) Numbers divisible by 2 are 2, 4 and 6

∴ Favourable outcomes are 3.

⇒ P_{(divisible by 2)} = 3/6 = 1/2.

**Question. A bag contains tickets, numbered 11, 12, 13, ....., 30. A ticket is taken out from the bag at random.**

**Find the probability that the number on the drawn ticket**

**(i) is a multiple of 7**

**(ii) is greater than 15 and a multiple of 5.**

**Answer :** Total number of tickets = 20 [∵ Numbers from 11 to 30 are 20]

(i) ∵ Multiples of 7 are 14, 21 and 28

∴ Number of favourable outcomes = 3

⇒ P_{(a multiple of 7)} = 3/20

(ii) ∵ The numbers that are greater than 15 and multiples of 5 are: 20, 25 and 30

∴ Number of favourable outcomes = 3

⇒ P_{(multiples of 5 and greater than 15)} = 3/20.

**Question. Two dice are thrown at the same time. Find the probability of getting different numbers on thedice. **

**Answer :** Since the two dice are thrown simultaneously.

∴ Total number of outcomes = 6 × 6 = 36

Number of outcomes for getting same numbers on both dice = 6

⇒ P (same numbers) = 6/36 = 1/6

Now, P (different numbers) + P (same numbers) = 1

⇒ P (different numbers) = 1 − P (same numbers)

= 1 −1/6

= 5/6.

**Question. Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10. **

**Answer :** When two different dice are rolled then possible outcomes are :

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

∴ Number of total outcomes = 36

∵ Sum of (5, 5), (6, 4) and (4, 6) is 10.

∴ No of favourable outcomes = 3

⇒ Required Probability = 3/36 or 1/12

**Question. A bag contains 5 red, 4 blue and 3 green balls. A ball is taken out of the bag at random. Find the probability that the selected ball is**

**(i) of red colour**

**(ii) not of green colour. **

**Answer :** Total number of balls = 5 + 4 + 3 = 12

⇒ Number of possible outcomes = 12

(i) ∵ Number of red balls = 5

∴ Favourable outcomes = 5

⇒ P_{(red ball)} = 5/12

(ii) ∵ Number of green balls = 3

∴ Number of ball which are not green = 12 − 3 = 9

⇒ Favourable outcomes = 9

∴ P_{(not green)} = 9/12 = 3/4.

**Question. A coin is tossed two times. Find the probability of getting at most one head.**

**Answer : **Since, the coin is thrown two times.

∴ Possible out comes = 4

Favourable outcomes are TT, TH, HT

i.e., Number of favourable outcomes = 3

∴ P_{(atmost one head)} = 3/4.

**Question. Two dice are thrown at the same time. Find the probability of getting same number on both dice.**

**Answer :** Total number of outcomes = 6 × 6 = 36

∴ Following are the outcomes that have same number on both dice are:

(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6)

∴ Favourable outcomes = 6

⇒ Required probability = 6/36 = 1/6.

**Question. A letter of English alphabet is chosen at random. Determine the probability that the letter is consonant.**

**Answer :** ∵ There are 26 letters of English alphabet

∴ Number of possible outcomes = 26

Since, there are 21 consonants of the English alphabets.

∴ Favourable outcomes = 21

⇒ Required probability = 21/26.

**Question. There are 40 students in class X of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card.**

**The cards being identical and she puts cards in a bag and stirs throughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a:**

**(i) girl **

**(ii) a boy**

**Answer :** Total number of students = 40

⇒ Number of possible outcomes = 40

(i) Q There are 25 girls in the class

∴ Number of favourable outcomes = 25

⇒ P(name of a girl) = 25/40 5/8

(ii) Q Number of boys = 15

∴ Number of favourable outcomes = 15

⇒ P(name of a boy) = 15/40 3/8

**Please click on below link to download CBSE Class 10 Maths Probabilty Worksheet**

CBSE Class 10 Mathematics Probability And Constructions Worksheet Set A |

CBSE Class 10 Maths Probabilty Worksheet |

#### Chapter 15 Probability CBSE Class 10 Mathematics Worksheet

The above practice worksheet for Chapter 15 Probability has been designed as per the current syllabus for Class 10 Mathematics released by CBSE. Students studying in Class 10 can easily download in Pdf format and practice the questions and answers given in the above practice worksheet for Class 10 Mathematics on a daily basis. All the latest practice worksheets with solutions have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their examinations. Studiestoday is the best portal for Printable Worksheets for Class 10 Mathematics students to get all the latest study material free of cost. Teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. After solving the questions given in the practice sheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics.

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