Class 10 Maths · Chapter 14

Probability

382 Class 10 Maths questions on Probability from the NCERT textbook, NCERT Exemplar and CBSE board papers 2015–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 14 of 20

1. Q261 CBSE 2023
   A box contains $20$ discs ​which are numbered from $1$ ​to $20$. If one disc is drawn at ​random from ​the ​box, then find the probability that the number on the ​drawn disc ​is a

   1. (i)$2$-digit number,
   2. (ii)number less than $10$.
   Show answer

   $P(\text{2-digit})=\frac{11}{20}$ and $P(<10)=\frac{9}{20}$

   Step-by-step solution →
2. Q262 CBSE 2023
   A bag ​contains $4$ ​red, $3$ ​blue and $2$ yellow balls. One ball is ​drawn at random from the ​bag. Find the probability ​that drawn ball is ​

   1. (i)red
   2. (ii)​yellow.
   Show answer

   $P(\text{red})=\frac{4}{9}$ and $P(\text{yellow})=\frac{2}{9}$.

   Step-by-step solution →
3. Q263 CBSE 2023
   From a well-shuffled deck of $52$ ​playing cards, ​all ​diamond ​cards are removed. ​Now, a card is drawn from the remaining pack at random. Find the probability ​that the selected ​card ​is a king.
   Show answer

   $P(\text{king})=\frac{1}{13}$

   Step-by-step solution →
4. Q264 CBSE 2023
   A die ​is rolled ​once. Find ​the probability ​of getting :

   1. (i)an even prime ​number.
   2. (ii)​a number greater than $4$. ​
   3. (iii)​an odd number.
   Show answer

   (i) $\frac{1}{6}$ (ii) $\frac{1}{3}$ (iii) $\frac{1}{2}$

   Step-by-step solution →
5. Q265 CBSE 2023
   Three different coins are ​tossed ​simultaneously. ​Find the ​probability of getting:

   1. (i)At ​least one ​head,
   2. (ii)At most two heads.

   1. iAt least one head[1]
   2. iiAt most two heads[2]
   Show answer

   (i) $\frac{7}{8}$, (ii) $\frac{7}{8}$

   Step-by-step solution →
6. Q266 CBSE 2023
   20 cards, numbered 1 to 20 are ​mixed thoroughly and then a card is drawn at random. Find the ​probability that ​the ​number on the ​drawn ​card is a multiple ​of ​3 or 5.
   Show answer

   $P=\frac{9}{20}$

   Step-by-step solution →
7. Q267 CBSE 2023
   Two dice are thrown simultaneously. ​Find ​the probability that ​the sum of ​the two ​numbers appearing on ​the top of the two dice is less than or equal to 10.
   Show answer

   $\frac{11}{12}$

   Step-by-step solution →
8. Q268 CBSE 2023
   A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Spinner I has three ​equal sectors Red (R), Green (G) and Yellow ​(Y). Spinner II has three equal sectors ​Red (R), ​Blue (B) and Green (G). Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) ​and another Blue (B), then ​you 'win'. ​One such outcome is ​written as 'RB'. Based on the above, answer the following questions :

   1. (i)List all possible outcomes of the game.[1]
   2. (ii)Find the probability of 'Making Purple'.[1]
   3. (iii) (a)For each win, a participant gets Rs 10, but if he/she loses, he/she has to pay Rs 5 to the school. If 99 participants played the game, calculate how much fund could the school have collected.[2]
   4. (iii) (b)If the same amount of Rs 5 has been decided for winning or losing the game, then how much fund had been collected by school ? (Number of participants = 99)[2]
   Show answer

   (i) 9 outcomes; (ii) $\frac{1}{9}$; (iii)(a) Rs 330; (iii)(b) Rs 385

   Step-by-step solution →
9. Q269 CBSE 2023
   There ​are $60$ students in class X of a school of which $45$ are girls and $15$ ​are boys. The class teacher has ​to ​select one student as a monitor. She ​writes ​the name of each student on a separate card and then mixes these cards after putting them in ​a box. She ​then draws a card at random from the box. Based on the above, answer the following questions:

   1. iWhat is the probability that the name on the selected card is of a girl student?
   2. iiWhat is the probability that the name on the selected card is of a boy student?
   3. iii-aIf there is one name Shivani, written on a card, what is the probability of her selection?
   4. iii-bOR What is the probability that one out of Ravi, Mahesh or Vikas is selected?
   Show answer

   (i) $3/4$; (ii) $1/4$; (iii)(a) $1/60$; (iii)(b) $1/20$.

   Step-by-step solution →
10. Q270 CBSE 2023
    Blood group describes the type of blood a ​person has. It is a classification of blood based on the presence or ​absence of ​inherited antigenic substances on the surface of red blood cells. ​Blood types predict whether a serious reaction will occur in a blood transfusion. In a sample of $50$ people, $21$ had type O blood, $22$ had ​type ​A, $5$ had ​type B and the rest had type AB blood group. Based on ​the above, answer the following questions.

    1. (i)What is the probability that a person chosen at random had type O blood?[1]
    2. (ii)What is the probability that a person chosen at random had type AB blood group?[1]
    3. (iii)What is the probability that a person chosen at random had neither type A nor type B blood group?[2]
    4. (iii OR)What is the probability that a person chosen at random had either type A or type B or type O blood group?[2]
    Show answer

    (i) $\frac{21}{50}$; (ii) $\frac{1}{25}$; (iii) $\frac{23}{50}$; (iii OR) $\frac{24}{25}$.

    Step-by-step solution →
11. Q271 CBSE 2023
    Computer-based learning (CBL) refers to any teaching ​methodology that makes use of computers for information transmission. ​At an elementary ​school level, computer applications can be used to display multimedia lesson plans. ​A survey was done on $1000$ elementary ​and secondary schools of Assam and they were classified by the ​number of computers they had. One school is chosen at ​random. Then answer the following questions:

    Survey of 1000 schools by number of computers

    Number of Computers	1 - 10	11 - 20	21 - 50	51 - 100	101 and more
    Number of Schools	250	200	290	180	80

    1. (i)Find the probability that the school chosen at random has more than $100$ computers.[1]
    2. (ii)(a)Find the probability that the school chosen at random has $50$ or fewer computers.[2]
    3. (ii)(b)Find the probability that the school chosen at random has no more than $20$ computers.[2]
    4. (iii)Find the probability that the school chosen at random has $10$ or less than $10$ computers.[1]
    Show answer

    (i) $\frac{2}{25}$; (ii)(a) $\frac{37}{50}$; (ii)(b) $\frac{9}{20}$; (iii) $\frac{1}{4}$.

    Step-by-step solution →
12. Q272 CBSE 2023
    Some students were asked ​to list ​their favourite colour. The measure of each ​colour is shown by the ​central angle of a pie chart given ​below. Study ​the pie ​chart and answer the following questions ​:

    Central angles for each favourite colour in the pie chart

    Colour	Central angle
    Green	$60^{\circ }$
    Blue	$60^{\circ }$
    Red	$30^{\circ }$
    Yellow	$90^{\circ }$
    White	$120^{\circ }$

    1. (i)If a student is chosen at random, then find the probability of his/her favourite colour being white ?[1]
    2. (ii)What is the probability of his/her favourite colour being blue or green ?[1]
    3. (iii)(a)If 15 students liked the colour yellow, how many students participated in the survey ?[2]
    4. (iii)(b) ORWhat is the probability of the favourite colour being red or blue ?[2]
    Show answer

    (i) $\frac{1}{3}$; (ii) $\frac{1}{3}$; (iii)(a) 60 students; (iii)(b) $\frac{1}{4}$.

    Step-by-step solution →
13. Q273 CBSE 2023
    "Eight Ball" ​is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and ​white. Of the ​15 numbered balls, eight are solid ​(non-white) coloured ​and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls ​(no cue ball) are placed in a large bowl and mixed, then one ball ​is drawn out ​at random.

    1. (i)What is the probability that the drawn ball bears number 8?[1]
    2. (ii)What is the probability that the drawn ball bears an even number? OR What is the probability that the drawn ball bears a number which is a multiple of 3?[2]
    3. (iii)What is the probability that the drawn ball is a solid coloured and bears an even number?[1]
    Show answer

    $P(8)=\frac{1}{15}$; $P(\text{even})=\frac{7}{15}$ (or multiple of 3 $=\frac{1}{3}$); $P(\text{solid and even})=\frac{4}{15}$

    Step-by-step solution →
14. Q274 CBSE 2020
    A ​card is drawn from a ​well shuffled deck of $52$ cards. ​The ​probability that it ​is a card of ​black colour ​is ​:

    1. (a)$\frac{1}{3}$
    2. (b)$\frac{1}{2}$
    3. (c)$\frac{1}{4}$
    4. (d)$\frac{3}{26}$
    Show answer

    (b) $\frac{1}{2}$

    Step-by-step solution →
15. Q275 CBSE 2020
    One card is drawn at random ​from a well-shuffled deck ​of $52$ ​cards. ​What ​is ​the probability of getting a ​Jack?

    1. (a)$\frac{3}{26}$
    2. (b)$\frac{1}{52}$
    3. (c)$\frac{1}{13}$
    4. (d)$\frac{3}{52}$
    Show answer

    (c) $\frac{1}{13}$

    Step-by-step solution →
16. Q276 CBSE 2020
    Two ​coins ​are ​tossed simultaneously. The ​probability ​of getting at ​most one head is

    1. (a)$\frac{1}{4}$
    2. (b)$\frac{1}{2}$
    3. (c)$\frac{2}{3}$
    4. (d)$\frac{3}{4}$
    Show answer

    (d) $\frac{3}{4}$

    Step-by-step solution →
17. Q277 CBSE 2020
    The probability that a ​number ​selected at random ​from the numbers $1,2,3,....,15$ is ​a multiple ​of $4$ is

    1. (a)$\frac{4}{15}$
    2. (b)$\frac{2}{15}$
    3. (c)$\frac{1}{15}$
    4. (d)$\frac{1}{5}$
    Show answer

    (d) $\frac{1}{5}$

    Step-by-step solution →
18. Q278 CBSE 2020
    A bag contains ​3 red, 5 ​black ​and 7 white ​balls. A ​ball ​is drawn from the bag at random. The probability that the ball drawn ​is not black, is

    1. (a)$\frac{1}{3}$
    2. (b)$\frac{9}{15}$
    3. (c)$\frac{5}{10}$
    4. (d)$\frac{2}{3}$
    Show answer

    (d) $\frac{2}{3}$

    Step-by-step solution →
19. Q279 CBSE 2020
    A dice ​is ​thrown ​once. The ​probability of ​getting ​an odd number ​is

    1. (a)$1$
    2. (b)$\frac{1}{2}$
    3. (c)$\frac{4}{6}$
    4. (d)$\frac{2}{6}$
    Show answer

    (b) $\frac{1}{2}$

    Step-by-step solution →
20. Q280 CBSE 2020
    The probability ​of ​an event ​that is ​sure ​to happen, is ​__________ .
    Show answer

    The probability of an event that is sure to happen is $1$.

    Step-by-step solution →