Source: CBSE · Competency Focused Practice Questions, Mathematics (Volume 2), Grade 10, pp. 19–31. Questions and answers are reproduced verbatim from the official CBSE document.
Try the question yourself before revealing the answer — that's how marks stick.
Q11 markMCQp. 19
A library receives a shipment for a series of encyclopedias. The shipment includes volumes 31 - 40. These encyclopedias arrived in a box and are not ordered.One encyclopedia is picked at random from the box without looking into it.What is the probability that the volume of the encyclopedia picked is a multiple of 2 OR 5?
Reveal official answer
Correct option: 3 — 6/10
Q21 markMCQp. 19
In basketball, different shots have varying point values – a two-point shot is taken from inside the three-point line, while a three-point shot is taken from outside the three-point line.In a basketball match, a player shot 5 three-point shots and 9 two-point shots out of the 35 shots he made.A particular shot he took was chosen at random. What is the probability that the shot that was chosen was NEITHER a three-point shot NOR a two-point shot?
Reveal official answer
Correct option: 3 — 3/5
Q31 markMCQp. 19
Jyoti and Dara are playing a game of tic-tac-toe. The probability of Jyoti winning the game is 0.7.What is the probability that Jyoti NOT winning the game?
Reveal official answer
Correct option: 3 — 0.3
Q41 markMCQp. 19
A card is drawn at random from a well shuffled standard deck of 52 cards.What is the probability that the card drawn is NEITHER a black card NOR a three?(Note: A deck of cards is divided into four suits - 2 black and 2 red. Each suit contains 13 ranks including numbered cards 2 through 10, and the face cards (jack, queen, king), along with the ace.)
Reveal official answer
Correct option: 2 — 24/52
Q51 markMCQp. 19
Matilda made the following pattern during art class:[square, ↑, circle, ↑, ↑, circle, square, hexagon, ↑, circle, square, hexagon, square] — 13 shapes in total (↑ = upward arrow shape).If she colours a shape at random, what is the probability that she will colour a circle?
Reveal official answer
Correct option: 3 — 3/13
Q61 markMCQp. 20
An apartment complex has 20 apartments of different sizes - 2BHK, 3BHK, 4BHK. The probability of a randomly picked apartment being a 3BHK is ⅖.How many 3BHK apartments are in the apartment complex?
Reveal official answer
Correct option: 4 — 8
Q71 markMCQp. 20
A box contains some new and weathered cricket balls of two colours. This data is shown in the table below.Colour \ Condition | New | WeatheredWhite | 5 | 5Red | 7 | 3Pratik picks a new, white ball and puts it back in the box.If a ball is then picked randomly from the box, what is the probability that it is NOT the same variety as Pratik picked?
Reveal official answer
Correct option: 4 — 15/20
Q81 markMCQp. 20
In a school, each student is assigned to one of the three houses- Honesty, Integrity and Courage. In a class of 43 students, 13 students are in Honesty house, 16 students are in Integrity house, and rest are in Courage house.If a student from this class is selected at random as a class representative, what is the probability that they belong to EITHER Integrity or Courage house?
Reveal official answer
Correct option: 4 — 30/43
Q91 markWrittenp. 20
Pritam is throwing a fair 6-sided die, with faces numbered from 1 to 6. Shown below are the outcomes of his first 4 throws:Throw 1 | Throw 2 | Throw 3 | Throw 46 | 6 | 6 | 6Pritam says, "The probability of getting a 6 in my next throw is higher than that of getting a different number on the die."Is Pritam's statement true or false? Give a valid reason.
Reveal official answer
• Writes that the statement is false. [0.5]
• Gives a valid reason. For example, when throwing a fair die, the probability of getting any one of the six numbers is the same. [0.5]
Q101 markWrittenp. 21
A pair of fair 6-sided dice with numbers 1-6 written on them are thrown.What is the probability that the sum of the numbers shown on the pair of dice is greater than 1? Justify your answer.
Reveal official answer
• Writes that all the possible sums on a pair of dice are greater than 1. [0.5]
• Finds the probability of the sum of the pair of dice being greater than 1 as 1. [0.5]
Q112 marksWrittenp. 21
Joel has exactly six 2-rupee coins, five 10-rupee coins and three 20-rupee coins in his pocket. He goes to the stationery store and buys a pen for Rs 19. He takes out a coin from his pocket at random.i) Find the probability that the coin will be sufficient to pay for the pen.ii) Find the probability that he will be able to give exactly Rs 19 to the shopkeeper.Show your work.
Reveal official answer
• i) Identifies total number of outcomes as 6 + 5 + 3 = 14 and number of favourable outcomes as 3. [0.5]
• Finds the probability that the coin will be sufficient to pay for the pen as 3/14. (Award full marks if the probability is found directly without writing step 1.) [0.5]
• ii) Writes that the probability that Joel will be able to give exactly Rs 19 to the shopkeeper is 0. [1]
Q122 marksWrittenp. 21
Roshni is playing a dart throwing game. In the game, players throw a dart at a wooden board from a safe distance. If the dart hits inside any one of the shaded circles, they score a point.[Figure: a rectangular board, 40 cm wide × 60 cm tall, with 3 shaded circles drawn on it — one near the top-centre and two side by side below it.](Note: The figure is not to scale.)The radius of each circle is 5 cm.Roshni is randomly throwing darts at the board. If each dart Roshni throws hits the board, what is the probability of her scoring a point?
Reveal official answer
• Finds the area of the rectangle board as 40 x 60 = 2400 cm². [0.5]
• Finds the area of the 3 circles with radius 5 unit as 3π(5)² = 75π cm². [0.5]
• Finds the probability of Roshni scoring a point as 75π/2400 = π/32. [1]
Q132 marksWrittenp. 22
Alisha had 4 orange candies, 4 mango candies, 2 cola candies and 1 strawberry candy in her bag. Neil only likes orange and cola candies. Alisha randomly takes out a candy to give to Neil.i) What is the probability that she gave Neil a candy that he likes?ii) What is the probability she gave Neil a mango candy?
Reveal official answer
• i) Finds that the probability of Alisha giving Neil a candy he likes is 6/11. [1]
• ii) Finds that the probability of Alisha giving Neil a mango candy is 4/11. [1]
Q142 marksWrittenp. 22
At an ice cream shop, there are two freezers, each containing different quantities of chocolate and vanilla flavoured ice creams as shown below.Flavour of Ice cream | Freezer 1 | Freezer 2Chocolate | 3 | 6Vanilla | 2 | 4Vikram won an offer to choose an ice cream at random from one of the freezers. He wants a vanilla ice cream.He believes that selecting from Freezer 2 is more likely to get him a vanilla ice cream because it has a higher number of them compared to Freezer 1.Is Vikram correct? Justify your answer.
Reveal official answer
• Writes that Vikram's statement is incorrect. [0.5]
• Justifies the answer. For example, writes that the probability of randomly picking a vanilla ice cream from Freezer 1 is 2/5 and the probability of randomly picking a vanilla ice cream from Freezer 2 is 4/10 which is the same as 2/5. Hence, the probability of picking a vanilla ice cream from Freezer 1 is the same as Freezer 2. [1.5]
Q152 marksWrittenp. 22
In a standard deck of 52 cards, a card is drawn without replacement. It is found to be a red 7.If another card is drawn, what is the probability that it is NOT a 7? Show your work.
Reveal official answer
• Finds the number of 7s in the remaining 51 cards as 3. [0.5]
• Finds the probability of drawing a 7 as 3/51 or 1/17. [0.5]
• Finds the probability of not drawing a 7 as 1 - 3/51 = 48/51 or 16/17. [1]
Q163 marksWrittenp. 22
The table below shows all the possible outcomes when two fair 6-sided dice are rolled together.1,1 | 1,2 | 1,3 | 1,4 | 1,5 | 1,62,1 | 2,2 | 2,3 | 2,4 | 2,5 | 2,63,1 | 3,2 | 3,3 | 3,4 | 3,5 | 3,64,1 | 4,2 | 4,3 | 4,4 | 4,5 | 4,65,1 | 5,2 | 5,3 | 5,4 | 5,5 | 5,66,1 | 6,2 | 6,3 | 6,4 | 6,5 | 6,6Study the table and find the probability for the following events.i) The numbers on both the dice are different.ii) The second die has a number greater than the first die.iii) The sum of both the dice is equal to 9.Show your work.
Reveal official answer
• i) Finds the probability of getting the same number is 30/36 or 5/6 [sic — printed thus in the official PDF]. [1]
• ii) Finds the probability of the second die having a number greater than the first die is 15/36 or 5/12. [1]
• iii) Finds the probability of getting the sum of both die to be equal to 9 is 4/36 or 1/9. [1]
Q173 marksWrittenp. 23
Akhila visits an indoor fishing area where an artificial pond is maintained. She randomly chooses a spot to catch fish. As she reached early, she is the only person fishing. The table below shows the population of the fish in the pond.Name of Fish | Population of FishIndian Carp | 24Rainbow Trout | 29Tilapia | 20Largemouth Bass | 30Catfish | 25Striped Bass | 22i) Find the probability of catching a Catfish.ii) Find the probability of catching a fish that is NOT a type of Bass.iii) She catches 2 Rainbow Trout on her first 2 attempts. What is the probability of her catching an Indian Carp on her 3rd attempt?Show your work.
Reveal official answer
• i) Finds the probability of catching a Catfish as 25/150 or 1/6. [1]
• ii) Finds the probability of not catching a type of Bass as (24+29+20+25)/150 = 98/150 or 49/75. [1]
• iii) Finds that the probability of catching an Indian Carp in her 3rd attempt as 24/148 or 6/37. [1]
Q183 marksWrittenp. 23
A fruit basket contains 3 oranges, 1 apple, 5 pomegranate and 6 bananas.i) Anirudh picks a fruit from the basket at random to eat. What is the probability that he picks an apple?ii) After Anirudh eats an apple, Aryan picks a fruit at random to eat. What is the probability that Aryan picks a banana?iii) After Anirudh and Aryan eat an apple and a banana respectively, Siddharth picks a fruit at random to eat. What is the probability that Siddharth picks an apple?
Reveal official answer
• i) Finds the probability of picking an apple as 1/15. [1]
• ii) Finds the probability of picking a banana after an apple has been eaten as 6/14 or 3/7. [1]
• iii) Finds the probability of picking an apple after an apple and a banana have been eaten as 0. [1]
Q195 marksWrittenp. 23
Anjali has a jar where she saves coins. She has collected twelve 2-rupee coins, and eighteen 10-rupee coins.One day, she added four 20-rupee coins to it. If a coin is picked at random from this jar now, without looking, find the probability that it is:i) a 1-rupee coinii) a 10-rupee coiniii) an even valued coiniv) anything EXCEPT a 5-rupee or a 20-rupee coin.Show your work.
Reveal official answer
• Finds the total coins in the jar as 12 + 18 + 4 = 34. [0.5]
• i) Finds the probability of picking a 1-rupee coin as 0. [1]
• ii) Finds the probability of picking a 10-rupee coin as 18/34 or 9/17. [1]
• iii) Finds the probability of picking an even valued coin as 1. [1]
• iv) Finds the probability of picking a 5-rupee as 0 and a 20-rupee coin as 4/34 or 2/17. Thus finds the probability of picking a 5-rupee or a 20-rupee coin as 2/17. [1]
• Finds the probability of not picking a 5-rupee or a 20-rupee coin as: 1 - 2/17 = 15/17. [0.5]
Q205 marksWrittenp. 24
Aisha and Ahmad are about to play a board game. To decide who starts first, they decide to throw two dice. The following was agreed upon:♦ Aisha goes first if the numbers on the dice are both prime numbers.♦ Ahmad goes first if the sum of the numbers on the dice equals 6.♦ They throw the dice repeatedly till one of these conditions is met.If the first throw has decided who goes first, who is more likely to start first? List all the outcomes and show your steps.
Reveal official answer
• Writes all the outcomes as {(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)} and indentifies the total number of outcomes as 36 [sic — printed thus in the official PDF]. [1.5]
• Writes the favourable outcomes for Aisha as {(2,2), (2,3), (2,5), (3,2), (3,3), (3,5), (5,2), (5,3), (5,5)} and identifies the total outcomes for Aisha to win as 9. Hence, finds the probability of Aisha getting both prime numbers as 9/36 or 1/4. [1.5]
• Writes the favourable outcomes for Ahmad as {(1,5), (2,4), (3,3), (4,2), (5,1)} and writes the total outcomes for Ahmad to win as 5. Finds the probability of Ahmad getting the sum of the numbers on the dice equals 6 as 5/36. [1.5]
• Writes that Aisha is more likely to start first. [0.5]
Q211 markWrittenp. 24
Answer the questions based on the given information.Sahiba conducted a survey in her school for 150 students of Class 10. She asked the students two multiple choice questions, which were "What time do you go to sleep at night?" and "What is your favourite subject?". Each student could choose only one option from the choices given.Sahiba tabulated the results from her survey as shown below.Sleep Schedule | English | Mathematics | Science | Social ScienceBefore 9 PM | 5 | 7 | 8 | 79 PM - 10 PM | 10 | 12 | 11 | 910 PM - 11 PM | 10 | 12 | 13 | 13After 11 PM | 7 | 8 | 10 | 8If a student is randomly selected, what is the probability that they sleep after 11 PM and that their favourite subject is NOT Social Science?
Reveal official answer
• Finds the probability that the randomly selected student goes to sleep after 11 PM and that their favourite subject is not Social Science as 25/150 or 1/6. [1]
Q221 markWrittenp. 24
Answer the questions based on the given information.Sahiba conducted a survey in her school for 150 students of Class 10. She asked the students two multiple choice questions, which were "What time do you go to sleep at night?" and "What is your favourite subject?". Each student could choose only one option from the choices given.Sahiba tabulated the results from her survey as shown below.Sleep Schedule | English | Mathematics | Science | Social ScienceBefore 9 PM | 5 | 7 | 8 | 79 PM - 10 PM | 10 | 12 | 11 | 910 PM - 11 PM | 10 | 12 | 13 | 13After 11 PM | 7 | 8 | 10 | 8If a student is randomly selected, what is the probability that they go to sleep after 10 PM?
Reveal official answer
• Finds the probability that the randomly selected student goes to sleep after 10 PM as 81/150 or 27/50. [1]
Q231 markWrittenp. 24
Answer the questions based on the given information.Sahiba conducted a survey in her school for 150 students of Class 10. She asked the students two multiple choice questions, which were "What time do you go to sleep at night?" and "What is your favourite subject?". Each student could choose only one option from the choices given.Sahiba tabulated the results from her survey as shown below.Sleep Schedule | English | Mathematics | Science | Social ScienceBefore 9 PM | 5 | 7 | 8 | 79 PM - 10 PM | 10 | 12 | 11 | 910 PM - 11 PM | 10 | 12 | 13 | 13After 11 PM | 7 | 8 | 10 | 8If a student is randomly selected, what is the probability that they go to sleep between 9 PM and 10 PM and that their favourite subject is Mathematics?
Reveal official answer
• Finds the probability that the randomly selected student has their favourite subject as Mathematics and go to sleep between 9 PM and 10 PM as 12/150 or 2/25. [1]
Q241 markWrittenp. 24
Answer the questions based on the given information.Sahiba conducted a survey in her school for 150 students of Class 10. She asked the students two multiple choice questions, which were "What time do you go to sleep at night?" and "What is your favourite subject?". Each student could choose only one option from the choices given.Sahiba tabulated the results from her survey as shown below.Sleep Schedule | English | Mathematics | Science | Social ScienceBefore 9 PM | 5 | 7 | 8 | 79 PM - 10 PM | 10 | 12 | 11 | 910 PM - 11 PM | 10 | 12 | 13 | 13After 11 PM | 7 | 8 | 10 | 8If a student is randomly selected, what is the probability that their favourite subject is English?
Reveal official answer
• Finds the probability that the randomly selected student's favourite subject is English as 32/150 or 16/75. [1]
Q251 markWrittenp. 24
Answer the questions based on the given information.Sahiba conducted a survey in her school for 150 students of Class 10. She asked the students two multiple choice questions, which were "What time do you go to sleep at night?" and "What is your favourite subject?". Each student could choose only one option from the choices given.Sahiba tabulated the results from her survey as shown below.Sleep Schedule | English | Mathematics | Science | Social ScienceBefore 9 PM | 5 | 7 | 8 | 79 PM - 10 PM | 10 | 12 | 11 | 910 PM - 11 PM | 10 | 12 | 13 | 13After 11 PM | 7 | 8 | 10 | 8If a student is randomly selected, what is the probability that they go to sleep before 10 PM and that their favourite subject is either Science or Social Science?
Reveal official answer
• If a student is randomly selected, what is the probability that they sleep before 10 PM and their favourite subject is either Science or Social Science as 35/150 or 7/30. [1]
Q262 marksWrittenp. 25
Answer the questions based on the given information.Gavin and Ishaan are playing a game using two fair dice, with faces numbered from 1-6. The rules of the game are given below:♦ Both players take turns to throw the dice, and note the sum of the numbers on both dice as their respective scores.♦ If a player gets the same number on both dice, they get exactly one extra turn to throw the dice again. The scores from both turns are then added to get the player's total score.♦ Once both players have thrown the dice, the person with the higher score wins. If the scores are equal, the game ends in a draw.Gavin begins by throwing the dice.What is the probability that he gets an extra turn? Show you work.
• Notes that Gavin will get an extra turn only when the dice show (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) or (6, 6). [0.5]
• Finds the probability of getting an extra turn as 6/36 or 1/6. [1]
Q271 markWrittenp. 25
Answer the questions based on the given information.Gavin and Ishaan are playing a game using two fair dice, with faces numbered from 1-6. The rules of the game are given below:♦ Both players take turns to throw the dice, and note the sum of the numbers on both dice as their respective scores.♦ If a player gets the same number on both dice, they get exactly one extra turn to throw the dice again. The scores from both turns are then added to get the player's total score.♦ Once both players have thrown the dice, the person with the higher score wins. If the scores are equal, the game ends in a draw.In one of the games, Gavin gets a score of 13.Find the probability that Ishaan wins the game if he plays only one turn. Justify your answer.
Reveal official answer
• Notes that the highest score possible in a single turn is 6 + 6 = 12.
Writes that there are no possible outcomes in which Ishaan gets a score higher than 13 in only one turn. Hence, the probability that Ishan wins is 0. [1]
Q282 marksWrittenp. 25
Answer the questions based on the given information.Gavin and Ishaan are playing a game using two fair dice, with faces numbered from 1-6. The rules of the game are given below:♦ Both players take turns to throw the dice, and note the sum of the numbers on both dice as their respective scores.♦ If a player gets the same number on both dice, they get exactly one extra turn to throw the dice again. The scores from both turns are then added to get the player's total score.♦ Once both players have thrown the dice, the person with the higher score wins. If the scores are equal, the game ends in a draw.If Gavin gets a score of 15 and Ishaan gets a pair of 6s on his first turn, find the probability of Ishaan winning the game on his second turn. Show your work.
Reveal official answer
• Finds the minimum sum required to win on the second turn as (15 - 2(6)) + 1 = (15 - 12) + 1 = 4. [0.5]
• Notes that Ishan will lose only if he gets a total less than 4, that is, if he gets (1, 1), (1, 2) or (2, 1). [0.5]
• Finds the probability of Ishaan winning on his second turn as 1 - 3/36 = 33/36 or 11/12. [1]
Q291 markWrittenp. 25
Answer the questions based on the given information.Shruti wrote numbers from 2 to 7 on six papers such that the number on each paper was unique. She divided the even and odd numbered papers into two groups, X and Y, respectively.She then chose a paper from each group at random, one after the other, without looking, and used the numbers written on them to form a 2-digit number. The number chosen first is written at the tens place of the 2-digit number.Find the probability that Shruti makes an even number less than 20.
Reveal official answer
• Reasons that a number less than 20 cannot be formed as the smallest number that can be formed is 23, thus finds its probability as 0. (Award full marks if all possible outcomes are listed and then probability is found.) [1]
Q302 marksWrittenp. 25
Answer the questions based on the given information.Shruti wrote numbers from 2 to 7 on six papers such that the number on each paper was unique. She divided the even and odd numbered papers into two groups, X and Y, respectively.She then chose a paper from each group at random, one after the other, without looking, and used the numbers written on them to form a 2-digit number. The number chosen first is written at the tens place of the 2-digit number.Shruti thought she is more likely to form an even number greater than 40 as compared to an odd number less than 40.Is she correct or incorrect? Justify your answer.
• Finds the probability of the number formed being an even number more than 40 as: 1/3.
Finds the probability of the number formed being an odd number less than 40 as: 1/6. [1]
Q312 marksWrittenp. 25
Answer the questions based on the given information.Shruti wrote numbers from 2 to 7 on six papers such that the number on each paper was unique. She divided the even and odd numbered papers into two groups, X and Y, respectively.She then chose a paper from each group at random, one after the other, without looking, and used the numbers written on them to form a 2-digit number. The number chosen first is written at the tens place of the 2-digit number.Shruti redistributed the 6 papers evenly between two new groups, A and B, making sure each group had a mix of even and odd numbered papers.Write one possible distribution of the papers in the two groups, group A and group B, such that the probability of forming an odd number is higher than that of forming an even number, if the paper from group A is chosen first. Give a valid reason.
Reveal official answer
• Finds any one such rearrangement of papers as: Group A: 2, 4, 7. Group B: 3, 5, 6. [1]
• Reasons that this arrangement of papers satisfies the mentioned condition and as group B has more odd numbered papers than even, the probability of getting an odd number will be higher in this rule. [1]