Class 10 Maths · Chapter 14

Probability

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

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 4 of 5

1. Q61 CBSE 2026
   A card ​is drawn ​from ​a well-shuffled deck ​of $52$ ​playing ​cards. The probability of getting a queen of ​spade is

   1. (a)$\frac{1}{26}$
   2. (b)$\frac{1}{52}$
   3. (c)$0$
   4. (d)$\frac{1}{4}$
   Show answer

   (b) $\frac{1}{52}$

   Step-by-step solution →
2. Q62 CBSE 2026
   Meena calculates that ​the probability ​of her winning the first ​prize in ​a lottery is $0.08$. If total $800$ ​tickets were ​sold, the number of ​tickets bought by her, is

   1. (a)$64$
   2. (b)$640$
   3. (c)$100$
   4. (d)$10$
   Show answer

   (a) $64$

   Step-by-step solution →
3. Q63 CBSE 2026
   Two ​dice ​are thrown simultaneously. ​The probability ​of ​getting ​a ​sum of $7$ is :

   1. (a)$\frac{2}{9}$
   2. (b)$\frac{1}{9}$
   3. (c)$\frac{5}{36}$
   4. (d)$\frac{1}{6}$
   Show answer

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

   Step-by-step solution →
4. Q64 CBSE 2026
   A card is drawn from a packet of $50$ identical cards ​numbered from $1$ ​to $50$. ​The probability of drawing ​a ​number which ​is a ​perfect square, ​is :

   1. (a)$\frac{7}{50}$
   2. (b)$\frac{8}{50}$
   3. (c)$\frac{6}{50}$
   4. (d)$\frac{10}{50}$
   Show answer

   (a) $\frac{7}{50}$

   Step-by-step solution →
5. Q65 CBSE 2026
   A die is ​thrown once. ​Probability of ​getting ​a ​number ​other ​than $3$ is :

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

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

   Step-by-step solution →
6. Q66 CBSE 2026
   The probability ​for a ​randomly selected number ​out ​of $1,2,3,4,\dots ,25$ ​to be ​a composite number is :

   1. (a)$\frac{15}{25}$
   2. (b)$\frac{10}{25}$
   3. (c)$\frac{11}{25}$
   4. (d)$\frac{9}{25}$
   Show answer

   (a) $\frac{15}{25}$

   Step-by-step solution →
7. Q67 CBSE 2026
   The probability ​of getting a sum of $7$, when ​two ​dice are ​thrown ​simultaneously, is ​:

   1. (a)$\frac{1}{9}$
   2. (b)$\frac{1}{12}$
   3. (c)$\frac{1}{6}$
   4. (d)$\frac{5}{36}$
   Show answer

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

   Step-by-step solution →
8. Q68 CBSE 2026
   An unbiased ​die ​is thrown once. The probability of getting an ​even ​prime ​number greater than 2 ​is :

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

   (d) $0$

   Step-by-step solution →
9. Q69 CBSE 2026
   From a bag ​containing yellow, ​red and green balls, ​the probability of drawing a yellow or ​red ​ball ​is equal ​to that of drawing a green ball. The probability of drawing a green ball from the ​bag is :

   1. (a)$\frac{1}{3}$
   2. (b)$\frac{1}{2}$
   3. (c)$1$
   4. (d)Not possible to find
   Show answer

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

   Step-by-step solution →
10. Q70 CBSE 2026
    In the ​question, ​a statement ​of Assertion (A) is followed by ​a ​statement of Reason (R). Choose the correct ​option.

    Assertion (A): The probability that a leap year has $53$ Mondays is $\frac{2}{7}$.

    Reason (R): The probability that a non-leap year has $53$ Mondays is $\frac{5}{7}$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (c) Assertion (A) is true, but Reason (R) is false.

    Step-by-step solution →
11. Q71 CBSE 2026
    Directions ​: ​In the following question, ​a statement of Assertion (A) is followed by a statement of ​Reason ​(R). Choose the correct ​option.

    Assertion (A): If probability of happening of an event is $0.2p$, $p>0$, then $p$ can't be more than $5$.

    Reason (R): $P(\overline{E})=1-P(E)$ for an event $E$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

    Step-by-step solution →
12. Q72 CBSE 2026
    Direction : In the following question, a statement of Assertion ​(A) ​is followed by ​a statement of ​Reason (R). Choose ​the ​correct option.

    Assertion (A): The probability of an event can not be $\frac{1}{0.9}$.

    Reason (R): $0\le P(E)\le 1$ for an event $E$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
13. Q73 CBSE 2026
    Assertion (A): From a bag containing $5$ red balls, $2$ white balls and $3$ green balls, the probability of drawing a non-white ball is $\frac{4}{5}$.

    Reason (R): For any event $E$, $P(E)+P(\text{not }E)=1$

    1. (a)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
14. Q74 CBSE 2026
    Select ​the correct ​answer from the ​codes ​(a), ​(b), ​(c) and (d) as given ​below.

    Assertion (A): The probability of a certain event $E$ is $1$.

    Reason (R): The sum of probabilities of all elementary events of an experiment is $1$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
15. Q75 CBSE 2026
    Assertion (A): The events “getting $2$” and “not getting $2$” in a single throw of an unbiased die are not equally likely events.

    Reason (R): The probability of getting $2$ in a single throw of an unbiased die is $\frac{1}{6}$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

    Step-by-step solution →
16. Q76 CBSE 2026
    In the following ​question, ​a ​statement ​of Assertion (A) is followed by ​a statement ​of Reason (R). Choose the correct ​option.

    Assertion (A): The probability that the date of birth of a man is in the month of June is $\frac{1}{12}$.

    Reason (R): There are $12$ months in a year.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true but Reason (R) is false.
    4. (d)Assertion (A) is false but Reason (R) is true.
    Show answer

    (d) Assertion (A) is false but Reason (R) is true.

    Step-by-step solution →
17. Q77 CBSE 2026
    Find the probability ​that ​a number ​selected at random ​from ​the numbers $30,31,32,33,\dots ,60$ is

    1. (i)a prime number
    2. (ii)​a multiple ​of $6$.
    Show answer

    (i) $P(\text{prime})=\frac{7}{31}$; (ii) $P(\text{multiple of }6)=\frac{6}{31}$.

    Step-by-step solution →
18. Q78 CBSE 2026
    Slips ​of letters ​of the word 'BACKGROUND' ​are ​put in a bowl and thoroughly mixed. One slip is picked up ​at random. Find the probability that picked up slip's letter ​is

    1. (i)a ​vowel
    2. (ii)present in the word 'BALL'.
    Show answer

    (i) The probability of a vowel is $\frac{3}{10}$. (ii) The probability the letter is present in 'BALL' is $\frac{2}{10}=\frac{1}{5}$.

    Step-by-step solution →
19. Q79 CBSE 2026
    All ​the red face cards ​are removed from a pack of $52$ playing cards. The ​remaining cards are well shuffled ​and then ​a card is ​drawn at random. Find the probability of getting a:

    1. (i)​red card
    2. (ii)​a king or queen
    Show answer

    (i) $P(\text{red card})=\frac{10}{23}$; (ii) $P(\text{king or queen})=\frac{2}{23}$.

    Step-by-step solution →
20. Q80 CBSE 2026
    A ​bag ​contains $25$ balls. ​Some of them are yellow ​and others are green. ​One ball ​is drawn at random. If probability of getting a green ball is $\frac{3}{5}$, then find the ​number of yellow balls.
    Show answer

    The number of yellow balls is $10$.

    Step-by-step solution →