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 13 of 20

1. Q241 CBSE 2023
   Which ​of ​the following ​numbers ​**cannot** be ​the probability of happening of an event ?

   1. (a)0
   2. (b)$\frac{7}{0.01}$
   3. (c)0.07
   4. (d)$\frac{0.07}{3}$
   Show answer

   (b) $\frac{7}{0.01}$

   Step-by-step solution →
2. Q242 CBSE 2023
   Lali ​tosses ​two ​different ​coins simultaneously. ​The ​probability ​that she ​gets at most one head is :

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

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

   Step-by-step solution →
3. Q243 CBSE 2023
   A girl ​calculates that the ​probability ​of her winning the first prize ​in a ​lottery is $0.08$. If $6000$ tickets ​are sold, ​how many tickets has she bought ​?

   1. (a)40
   2. (b)240
   3. (c)480
   4. (d)750
   Show answer

   (c) 480

   Step-by-step solution →
4. Q244 CBSE 2023
   The probability ​that a ​leap year ​selected at random will contain $53$ ​Sundays ​and $53$ Mondays, is:

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

   (a) $\frac{1}{7}$

   Step-by-step solution →
5. Q245 CBSE 2023
   An ​unbiased ​die is thrown. The ​probability ​of ​getting an odd prime ​number ​is

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

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

   Step-by-step solution →
6. Q246 CBSE 2023
   A card is drawn ​at random ​from a well-shuffled pack ​of 52 ​cards. The probability that the card ​drawn is not an ​ace is :

   1. (a)$\frac{1}{13}$
   2. (b)$\frac{9}{13}$
   3. (c)$\frac{4}{13}$
   4. (d)$\frac{12}{13}$
   Show answer

   (d) $\frac{12}{13}$

   Step-by-step solution →
7. Q247 CBSE 2023
   A number ​is ​chosen from the ​numbers 1, 2, 3 and denoted as $x$, and ​a number is chosen ​from the numbers 1, ​4, ​9 and denoted as $y$. Then $P(xy<9)$ is :

   1. (a)$\frac{1}{9}$
   2. (b)$\frac{3}{9}$
   3. (c)$\frac{5}{9}$
   4. (d)$\frac{7}{9}$
   Show answer

   (c) $\frac{5}{9}$

   Step-by-step solution →
8. Q248 CBSE 2023
   In a ​group of $20$ people, $5$ can't swim. ​If one person ​is selected ​at random, then ​the ​probability that ​he/she can swim, is

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

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

   Step-by-step solution →
9. Q249 CBSE 2023
   The probability ​for a randomly ​selected number ​out ​of $1,2,3,4,\dots ,25$ ​to ​be a prime number ​is:

   1. (a)$\frac{8}{25}$
   2. (b)$\frac{10}{25}$
   3. (c)$\frac{11}{25}$
   4. (d)$\frac{9}{25}$
   Show answer

   (d) $\frac{9}{25}$

   Step-by-step solution →
10. Q250 CBSE 2023
    Directions: A ​statement of Assertion (A) is followed by ​a statement ​of ​Reason ​(R). Choose the ​correct ​option.

    Assertion (A): Two players, Sania and Ashnam play a tennis match. The probability of Sania winning the match is 0.79 and that of Ashnam winning the match is 0.21.

    Reason (R): The sum of probabilities of two complementary events 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 →
11. Q251 CBSE 2023
    Assertion-Reason type ​question. ​Choose the correct option about ​the Assertion (A) and the ​Reason (R) ​given ​below.

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

    Reason (R): The probability that a non-leap year has $53$ Sundays is $\frac{1}{7}$.

    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. Q252 CBSE 2023
    Assertion (A): When two coins are tossed together, the probability of getting no tail is $\frac{1}{4}$.

    Reason (R): The probability $P(E)$ of an event $E$ satisfies $0\le P(E)\le 1$.

    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

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

    Step-by-step solution →
13. Q253 CBSE 2023
    Assertion (A): The probability that a leap year has 53 Sundays is $\frac{2}{7}$.

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

    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 and 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

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

    Step-by-step solution →
14. Q254 CBSE 2023
    Directions: ​A statement ​of Assertion (A) is ​followed ​by a statement of ​Reason (R). ​Choose the ​correct option.

    Assertion (A): The probability of getting a prime number, when a die is thrown once, is $\frac{2}{3}$.

    Reason (R): On the faces of a die, prime numbers are $2,3,5$.

    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 →
15. Q255 CBSE 2023
    Directions: A statement ​of Assertion ​(A) is followed by ​a statement ​of Reason ​(R). ​Choose the ​correct option.

    Assertion (A): A fair die is thrown once. The probability of getting a prime number is $\frac{1}{2}$.

    Reason (R): A natural number is a prime number if it has only two factors.

    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 →
16. Q256 CBSE 2023
    Directions: A statement ​of Assertion ​(A) ​is followed ​by ​a ​statement of Reason (R). Choose ​the ​correct option.

    Assertion (A): An event is very likely to happen if its probability is $0.9999$.

    Reason (R): Probability of a sure event is always $1$.

    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

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

    Step-by-step solution →
17. Q257 CBSE 2023
    Read the Assertion ​(A) and ​the Reason ​(R) ​and ​choose ​the correct option.

    Assertion (A): The probability of getting a doublet in a single throw of a pair of dice is $\frac{1}{6}$.

    Reason (R): For any event $A$, $0\le P(A)\le 1$.

    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

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

    Step-by-step solution →
18. Q258 CBSE 2023
    Directions: A statement of Assertion (A) is ​followed ​by a statement of Reason ​(R). ​Choose the ​correct ​option.

    Assertion (A): The probability of randomly drawing a card with an even number from a box containing cards numbered 1 to 100 is $\frac{1}{2}$.

    Reason (R): $P(\text{event})=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$.

    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 →
19. Q259 CBSE 2023
    Three ​coins are tossed together.

    1. (i)Write all ​possible ​outcomes.
    2. (ii)Find ​the ​probability of having at most $2$ heads.

    1. (i)Write all possible outcomes.[1]
    2. (ii)Find the probability of having at most 2 heads.[1]
    Show answer

    Outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT; $P(\text{at most }2\text{ heads})=\frac{7}{8}$.

    Step-by-step solution →
20. Q260 CBSE 2023
    If ​a ​fair ​coin is tossed twice, find ​the probability ​of ​getting ​'atmost one head'.
    Show answer

    $\frac{3}{4}$

    Step-by-step solution →