Assignments for Class 10 Mathematics Probability have been developed for Standard 10 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 10 Mathematics Probability from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 10 Mathematics Probability. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Probability book and get good marks in class 10 exams.

**Question. 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? **

(A) 1/2

(B) 2/5

(C) 8/15

(D) 9/20

**Answer**

D

**Question. Three coins are tossed, the probability of getting at most 2 heads is **

(A) 3/8

(B) 1/2

(C) 7/8

(D) 1/8

**Answer**

C

**Question. What is the probability of getting a sum 9 from two throws of a dice? **

(A) 1/6

(B) 1/8

(C) 1/9

(D) 1/12

**Answer**

C

**Question. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? **

(A) 1/2

(B) 3/4

(C) 3/8

(D) 5/16

**Answer**

B

**Question. Two dice are tossed. The probability that the total sum is a prime number is: **

(A) 1/6

(B) 5/12

(C) 1/2

(D) 7/9

**Answer**

B

**Question. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is: **

(A) 1/13

(B) 2/13

(C) 1/26

(D) 1/52

**Answer**

C

**Question. Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and other is a heart, is : **

(A) 3/20

(B) 29/34

(C) 47/100

(D) 13/102

**Answer**

D

**Question. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)? **

(A) 1/13

(B) 3/13

(C) 1/4

(D) 9/52

**Answer**

B

**Question. There are 30 cards of the same size in a bag on which natural numbers 1 to 30 are written. One card is taken out of the bag at random. Then the probability that the number on the selected card is not divisible by 3 is **

(A) 1/3

(B) 3/4

(C) 2/3

(D) 1/4

**Answer**

C

**Question. If all the face cards are removed from a pack of 52 cards and then a card is randomly drawn then the probability of getting a ‘10 of heart’ will be **

(A) 1/40

(B) 2/49

(C) 3/40

(D) 3/17

**Answer**

A

**Question. The probability of guessing the correct answer to a certain question is p/12. If the probability of not guessing the correct answer to the same question is 3/4, the value of p is **

(A) 3

(B) 4

(C) 2

(D) 1

**Answer**

A

**Question. From a well shuffled pack of 52 cards, black aces and black queens are removed and from the remaining cards, a card is drawn at random. Then the probability of drawing a king or a queen is **

(A) 7/8

(B) 3/4

(C) 1/8

(D) 1/2.

**Answer**

C

**Question. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is: **

(A) 21/46

(B) 25/117

(C) 1/50

(D) 3/25

**Answer**

A

**Question. A dice is tossed 100 times and the data is recorded as below ****The probability that we get at even number in a trial is**

(A) 2/5

(B) 3/5

(C) 1/5

(D) 4/5

**Answer**

A

**Question. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? **

(A) 1/15

(B) 25/57

(C) 35/256

(D) 1/221

**Answer**

D

**Question. The king, queen and jack of hearts are removed from a deck of 52 playing cards and then well shuffled. One card is selected from the remaining cards. Then the probability of getting a king is **

(A) 1/49

(B) 2/49

(C) 3/49

(D) 1

**Answer**

A

**Question. Sum of probabilities of all the events in a sample space related to any event is **

(A) 1

(B) 0

(C) –1

(D) not defined

**Answer**

A

**VERY SHORT ANSWER TYPE QUESTIONS**

**Question. A card is drawn at random from a pack of 52 playing cards. What is the probability that the card drawn is neither a red card nor a black king?**

**Answer**

6/13

**Question. A child has a die whose six faces show the letters as given below : **

**The die is throw once. What is the probability of getting ‘B’?**

**Answer**

1/3

**Question. A die is thrown once. What is the probability of getting a prime number?**

**Answer**

1/2

**Question. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is four times that of a red ball, how many blue balls are in the bag?**

**Answer**

20

**Question. A letter is chosen from the word ‘RANDOM’. What is the probability that it is a vowel?**

**Answer**

1/3

**Question. Out of 200 bulbs in a box, 20 bulbs are defective. One bulb is taken out at random from the box. What is the probability that the drawn bulb is not defective?**

**Answer**

9/10

**Question. Three coins are tossed simultaneously. What is the probability of getting no head?**

**Answer**

1/8

**Question. A coin is tossed twice. Write the possible outcomes.**

**Answer**

{HH, HT, TH, TT}

**Question. Two dice are thrown simultaneously. What is the probability of getting a doublet?**

**Answer**

1/6

**Question. A bag contains 6 red and 4 blue balls. One ball is drawn at random. What is the probability that the ball drawn is not red?**

**Answer**

2/5

**Question. A die is rolled twice. Write the possible outcomes.**

**Answer**

{(1, 1), (1, 2),…., (1, 6), (2, 1),…., (2, 6),….., (6, 1),……, (6, 6)}; Total 36 cases.

**Question. If the probability of winning a game is 0.4. What is the probability of losing it?**

**Answer**

0.6

**Question. Two dice are thrown simultaneously. What is the probability of getting a multiple of 3 as the sum?**

**Answer**

1/3

**Question. Two coins are tossed simultaneously. What is the probability of getting atleast one head?**

**Answer**

3/4

**Question. A box contains 30 cards, numbered from 1 to 30. One card is drawn at random from the box. What is the probability that the number on the drawn card is a multiple of 2 or 3?**

**Answer**

2/2

**Probability**

Different types of events and their probability representation

- Sure Events (PE) =1
- Impossible Event ,(PE) =0
- Certain Events,0 ≤ (PE) ≤ 1
- Elementary Events, (An event having only one outcome)
- Complementary Event,

**Relationship between events**

**Question. Three unbiased coins are tossed together. Find the probability of getting :****(i) all heads (ii) two heads****(iii) one head (iv) at least two heads****Solution.** Here, possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH and TTT.

So, total no. of possible outcomes = 8

(i) favourable outcome = HHH

So, No. of favourable outcome = 1

∴ P (all heads) = no. of favourable outcomes / Total no. possible outcome = 1/8

(ii) favourable outcomes are HHT, THH and HTH.

So, no. of favourable outcomes = 3

∴ P (two heads) = 3/8

(iii) favourable outcomes are HTT, THT and TTH.

So, no. of favourable outcomes = 3

∴ P (one head) = 3/8

(iv) favourable outcomes are HHH, HHT, HTH and THH.

So, no. of favourable outcomes = 4

∴ P (at least two heads) = 4/8 = 1/2

**Question. Find the probability that a leap year selected at random will contain 53 sundays.****Solution.** In a leap year, there are 366 days.

We have, 366 days = 52 weeks + 2 days.

Thus, a leap year has always 52 sundays.

The remaining 2 days can be :

(i) Sunday and Monday

(ii) Monday and Tuesday

(iii) Tuesday and Wednesday

(iv) Wednesday and Thursday

(v) Thursday and Friday

(vi) Friday and Saturday

(vii) Saturday and Sunday

Clearly, there are seven elementary events associated with this random experiment.

Let E be the event that a leap year has 53 sundays. Clearly, the event E will happer if the last two days of the leap year are either Sunday and Monday or Saturday and Sunday.

∴ Favourable no. of elementary events = 2

Hence, required probability = 2/7 Ans.

**PRACTICE EXERCISE**

**Question. A girl calculates that the probability of her winning the third prize in a lottery is 0.08. If 6000 tickets are sold, how many ticket has she bought.****Solution.** 480

**Question. What is probability that a non-leap year selected at random will contain 53 Sundays.****Solution.** 1/7

**Question. In a lottery, there are10 prizes and 25 blanks. Find the probability of getting a prize.****Solution.** 2/7

**Question. Find the probability of prime numbers selected at random from the numbers 3,4,5,6…25 .****Solution.** 8/23

**Question. A bag contains 5 red, 4 blue and 3 green balls. A ball is taken out from the bag at random. Find the probability that the selected ball is (a) of red colour (b) not of green colour.****Solution.** A. 5/12 B. 3/4

**Question. A jar contains 54 marbles each of which is blue ,green or white . The probability of selecting a blue marble at random from the jar is 1/3, and the probability of selecting a green marble at random is 4/9 . How many white marbles does the jar contain.****Solution.** 12

**Question. two coins are tossed simultaneously. Find the probability of getting exactly one head.****Solution.** 1/2

**Question. A dice is thrown once. What is the probability of getting a number greater than 4?****Solution.** 1/3

**Question. The probability of getting bad egg in a lot of 400 is 0.035. Then find the number of bad eggs in the lot.****Solution.** 14

**Question. Write the probability of a sure event.****Solution.** 1

**Question. Cards with numbers 2 to 101 are placed in a box. A card selected at random from the box. Find the probability that the card which is selected has a number which is a perfect square.****Solution.** 9/100

**Question. Two dice are thrown at the same time. Find the probability that the sum of two numbers appearing on the top of the dice is more than 9.****Solution.** 1/6

**Question. Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.****Solution.** 5/6

**Question. Cards marked with the number 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from the box. Find the probability that the number on the card is:****(i) An even number****(ii) A number less than14****(iii) A number is perfect square****(iv) A prime number less than 20****Solution.** A. 1/2 B. 3/25 C. 9/100, D. 2/25

**Question. A coin is tossed two times. Find the probability of getting almost one head.****Solution.** 3/4

**Question. What is the probability of an impossible event?****Solution.** 0

**Question. When a dice is thrown, and then find the probability of getting an odd number less than 3.****Solution.** 1/6

**Question. A bag contains card which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears.****a.) A Two digit number****b.) A number which is perfect square.****Solution.** 81/89, 8/89

**Question. Two dice are thrown at the same time. Find the probability of getting (a) same no. on the both side(b) different no. on both dices.****Solution.** A. 1/6 B. 5/6

**Question. Find the probability of getting the letter M in the word “MATHEMATICS”.****Solution.** 2/11

**Question. Two dice are thrown simultaneously. Find the probability of getting :****(i) a doublet i.e. same number on both dice.****(ii) the sum as a prime number.****Solution.** Possible outcomes associated to the random experiment of throwing two dice are :

(1, 1), (1, 2), ……., (1, 6)

(2, 1), (2, 2), ……., (2, 6)

…………………………………

…………………………………

(6,1) , (6, 2), ……., (6, 6)

∴ Total number of possible outcomes = 6 × 6 = 36

(i) The favourable outcomes are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).

∴ Total no. of favourable outcomes = 6

So, P(a doublet) = no. of favourable outcomes / Total no. of possible outcomes

= 6/36 = 1/6

(ii) Here, favourable sum (as a prime number) are 2, 3, 5, 7 and 11.

So, favourable outcomes are (1, 1), (1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (1, 6), (6, 1), (2, 5), (5, 2),

(3, 4), (4,3), (6, 5) and (5, 6).

∴ no. of favourable outcomes = 15

∴ P (the sum as a prime number) = 15/36 = 5/12 Ans.

**Question. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn.****Find the probability that the card drawn is :****(i) an ace (ii) either red or king****(iii) a face card (iv) a red face card****Solution.** here, total no. of possible outcomes = 52.

(i) There are 4 ace cards in a pack of 52 cards. One ace can be chosen in 4 ways.

So, favourable no. of outcomes = 4

∴ P (an ace) = no. of favourable outcomes / Total no. of possible outcomes

= 4/52 = 1/13

(ii) There are 26 red cards, including 2 red kings. Also, there are 4 kings, two red and two black.

∴ card drawn will be a red card or a king if it is any one of 28 cards (26 red cards and 2 black kings)

So, favourable no. of outcomes = 28

∴ P(either red or king) = 28/52 = 7/13

(iii) Kings, queens and jacks are the face cards.

So, favourable no. of outcomes = 3 × 4 = 12

∴ P(a face card) = 12/52 = 7/13

(iv) There are 6 red face cards, 3 each from diamonds and hearts.

So, favourable no. of outcomes = 6

∴ P(a red face card) = 6/52 = 3/26

**Question. An unbiased die is thrown. What is the probability of getting :****(i) an odd number (ii) a multiple of 3****(iii) a perfect square number (iv) a number less than 4.****Solution.** Here, total number of all possible outcomes= 6

(i) favourable outcomes are 1, 3, 5.

So, no. of favourable outcomes = 3

∴ P (an odd number) = No. of favourable outcomes / Total no. of possible outcome = 3/6 = 1/2

(ii) favourable outcomes are 3 and 6.

So, no. of favourable outcomes = 2

∴ P (a multiple of 3) = 2/6 = 1/3

(iii) favourable outcomes are 1 and 4.

So, no. of favourable outcomes = 2

∴ P (a perfect square number) = 2/6 = 1/3

(iv) favourable outcomes are 1, 2 and 3.

So, no. of favourable outcomes = 3

∴ P (a number less than 4) = 3/6 = 1/2

**Question. Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is ****drawn from this box. Find the probability that the number of the card is :****(i) an even number (ii) a number less than 14****(iii) a number which is a perfect square (iv) a prime number less than 20.****Solution.** From 2 to 101, these are (101–2) + 1 = 100 numbers.

So, total no. of possible outcomes = 100.

(i) From 2 to 101, the even numbers are 2, 4, 6, …., 100 which are 50 in number.

So, number of favourable outcomes = 50

∴ P(an even number) = no. of favourable outcomes / Total no. of possible outcomes

= 50/100 = 1/2

(ii) From 2 to 101, the numbers less than 14 are 2, 3, …., 13 which are 12 in number.

So, no. of favourable outcomes = 12

∴ P(a number less than 14) = 12/100 = 3/25

(iii) From 2 to 101, the perfect squares are 4, 9, 16, ….. 100, which are 9 in number.

So, no. of favourable outcomes = 9

∴ P (a number which is a perfect square) = 9/100

(iv) From 2 to 101, the prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17 and 19 which are 8 in number.

So, no. of favourable outcomes = 8

∴ P (a prime no. less than 20) = 8/100 = 2/25

**Question. A bag contains 3 red balls and 5 black balls.A ball is drawn at random from a bag. What is the probability that the ball drawn is :****(i) red (ii) not red ****Solution.** Total number of balls = 3 + 5 = 8

(i) P (red ball) = no. of red balls / Total no.of balls = 3/8

(ii) P (not red ball) = 1 – P(red ball) = 1 – 3/8 = 5/8

**Question. Suppose you drop a die at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter 1 m? **

**Solution.** Total area of rectangular region = 3 m × 2 m = 6 m^{2}

**Question. A bag contains 12 balls out of which x are white.****(i) If one ball is drawn at random, what is the probability that it will be a white ball?****(ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in (i). Find x.****Solution.** (i) Total number elementary events = 12.

There are x white balls out of which one can be chosen in x ways.

So, favourable number of elementary events = x

∴ p_{1} = P (white ball) = no. of favourable outcomes / Total no. of possible outcomes

= x / 12

(ii) If 6 more white balls are put in the bag, then total number of balls in the bag =12 + 6 = 18 and, no. of white balls in the bag = x + 6

∴ p_{2} = p (getting a white ball) = x + 6 / 18

It is given that, p_{2} = 2p_{1}

⇒ x + 6 /18 = 2x x / 12

⇒ x + 6 /18 = x / 6 ⇒ 6( x+ 6) = 18 x

⇒ 6x + 36 = 18x ⇒ 12 x = 36 ⇒ x = 3 Ans.

**Question. A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3 . Find the number of blue marbles in the jar.****Solution.** Total number of elementary events = 24.

Let there be x green marbles.

∴ P (green marbles is drawn) = x / 24

but, P(green marbles is drawn) = 2/3 (given)

⇒ x/24 = 2/3 ⇒ x = 2/3 x 24 ⇒ x = 16

∴ Number of green marbles = 16

⇒ Number of blue marbles = 24 – 16 = 8 Ans.

## Assignments for Class 10 Mathematics Probability as per CBSE NCERT pattern

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