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 7 of 20

1. Q121 CBSE 2025
   Two coins ​are ​tossed ​simultaneously. ​The ​probability ​of getting at ​least one head is

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

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

   Step-by-step solution →
2. Q122 CBSE 2025
   A fair die is thrown ​once. The probability ​of ​getting ​an even number ​less ​than $3$ is :

   1. (a)$\frac{1}{6}$
   2. (b)$\frac{1}{3}$
   3. (c)$\frac{1}{2}$
   4. (d)$0$
   Show answer

   (a) $\frac{1}{6}$

   Step-by-step solution →
3. Q123 CBSE 2025
   If ​probability ​of happening of an event is $57\%$, ​then probability ​of non-happening of the event ​is

   1. (a)$0.43$
   2. (b)$0.57$
   3. (c)$53\%$
   4. (d)$\frac{1}{57}$
   Show answer

   (a) $0.43$

   Step-by-step solution →
4. Q124 CBSE 2025
   A ​black card ​is lost from a deck ​of 52 playing cards. ​Rest of the cards are shuffled and one card is drawn at random from the available cards. ​The probability ​that the ​drawn card is ​king of hearts, is

   1. (a)$\frac{1}{52}$
   2. (b)$\frac{1}{4}$
   3. (c)$\frac{1}{51}$
   4. (d)$\frac{1}{26}$
   Show answer

   (c) $\frac{1}{51}$

   Step-by-step solution →
5. Q125 CBSE 2025
   The probability of ​the happening of an event is 'p' and the ​probability of ​non-happening of the same event ​is 'q'. The ​relation between 'p' and 'q' ​is ​:

   1. (a)$p+q+1=0$
   2. (b)$p=q-1$
   3. (c)$p+q=1$
   4. (d)$p=1,q=1$
   Show answer

   (c) $p+q=1$

   Step-by-step solution →
6. Q126 CBSE 2025
   In a cricket match, a batsman hits the boundary $7$ times out ​of the $42$ balls ​he plays. The ​probability ​of his **not** hitting a ​boundary is ​:

   1. (a)$\frac{1}{7}$
   2. (b)$\frac{2}{7}$
   3. (c)$\frac{5}{6}$
   4. (d)$\frac{1}{6}$
   Show answer

   (c) $\frac{5}{6}$

   Step-by-step solution →
7. Q127 CBSE 2025
   If $E$ is an event ​such that $P(E)=0.1$, ​then $P(\overline{E})$ is ​equal ​to

   1. (a)$0.9$
   2. (b)$\frac{1}{2}$
   3. (c)$0.99$
   4. (d)$-1$
   Show answer

   (a) $0.9$

   Step-by-step solution →
8. Q128 CBSE 2025
   Three coins are tossed ​together. The ​probability that exactly one ​coin ​shows ​head, is

   1. (a)$\frac{1}{8}$
   2. (b)$\frac{1}{4}$
   3. (c)$1$
   4. (d)$\frac{3}{8}$
   Show answer

   (d) $\frac{3}{8}$

   Step-by-step solution →
9. Q129 CBSE 2025
   A ​card is drawn at ​random ​from a well shuffled deck of $52$ ​playing ​cards. The probability that drawn ​card shows number '9' is :

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

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

   Step-by-step solution →
10. Q130 CBSE 2025
    A card ​is selected ​at random ​from a deck of ​52 playing cards. The probability ​of it being ​a red face card is :

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

    (d) $\frac{3}{26}$

    Step-by-step solution →
11. Q131 CBSE 2025
    Two ​dice are ​thrown simultaneously and the ​product of the numbers appearing on the ​tops ​is noted. The probability of the product to be ​less than ​6 is ​:

    1. (a)$\frac{1}{6}$
    2. (b)$\frac{1}{4}$
    3. (c)$\frac{5}{18}$
    4. (d)$\frac{7}{18}$
    Show answer

    (c) $\frac{5}{18}$

    Step-by-step solution →
12. Q132 CBSE 2025
    A die ​is thrown once. The probability of getting ​a number ​which ​is $\text{not}$ ​a ​factor of $36$, is ​:

    1. (a)$\frac{1}{2}$
    2. (b)$\frac{2}{3}$
    3. (c)$\frac{1}{6}$
    4. (d)$\frac{5}{6}$
    Show answer

    (c) $\frac{1}{6}$

    Step-by-step solution →
13. Q133 CBSE 2025
    Two ​dice are ​rolled together. ​The probability that only ​one die ​shows number 4, is

    1. (a)$\frac{11}{36}$
    2. (b)$\frac{1}{3}$
    3. (c)$\frac{5}{18}$
    4. (d)$\frac{1}{4}$
    Show answer

    (c) $\frac{5}{18}$

    Step-by-step solution →
14. Q134 CBSE 2025
    The probability that a $2$-digit ​number ​less than $20$, selected at random will ​be a multiple ​of $2$ and ​not ​a ​multiple of $3$, is

    1. (a)$\frac{1}{2}$
    2. (b)$\frac{1}{5}$
    3. (c)$\frac{3}{10}$
    4. (d)$\frac{3}{11}$
    Show answer

    (c) $\frac{3}{10}$

    Step-by-step solution →
15. Q135 CBSE 2025
    The ​probability ​of ​getting a composite number greater than 3 ​on throwing a die ​is

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

    (b) $\frac{1}{3}$

    Step-by-step solution →
16. Q136 CBSE 2025
    A pair of dice ​is thrown simultaneously. Let $E$ ​denote ​the ​event that 'The sum of ​numbers ​obtained on both dice is at least $9$.' The number of ​outcomes in favour of event $E$ is :

    1. (a)4
    2. (b)6
    3. (c)10
    4. (d)26
    Show answer

    (c) 10

    Step-by-step solution →
17. Q137 CBSE 2025
    The total ​number of ​outcomes in the ​experiment ​of simultaneous throw of ​three ​dice is :

    1. (a)6
    2. (b)18
    3. (c)36
    4. (d)216
    Show answer

    (d) 216

    Step-by-step solution →
18. Q138 CBSE 2025
    A pair ​of dice is ​thrown. The ​probability that sum of numbers ​appearing ​on ​top ​faces is ​at most $10$ is:

    1. (a)$\frac{1}{11}$
    2. (b)$\frac{10}{11}$
    3. (c)$\frac{5}{6}$
    4. (d)$\frac{11}{12}$
    Show answer

    (d) $\frac{11}{12}$

    Step-by-step solution →
19. Q139 CBSE 2025
    In a ​random ​experiment of throwing a die, which ​of ​the following ​is ​a ​sure event?

    1. (a)Getting a number between 1 and 6
    2. (b)Getting an odd number $<7$
    3. (c)Getting an even number $<7$
    4. (d)Getting a natural number $<7$
    Show answer

    (d) Getting a natural number $<7$

    Step-by-step solution →
20. Q140 CBSE 2025
    A bag ​contains $40$ ​balls out of which some are red, some are blue ​and the remaining are black. If the probability of drawing a ​red ball from the bag is $\frac{11}{20}$ and that of blue ​ball is $\frac{1}{5}$, then ​the number of black ​balls in the bag are:

    1. (a)$5$
    2. (b)$15$
    3. (c)$20$
    4. (d)$10$
    Show answer

    (d) $10$

    Step-by-step solution →