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 11 of 20

1. Q201 CBSE 2024
   $Assertion(A):$ The probability of getting ​number 8 ​on rolling ​a die is zero (0). $Reason(R):$ ​The probability ​of ​an impossible event ​is zero (0).

   Assertion (A): The probability of getting number 8 on rolling a die is zero (0).

   Reason (R): The probability of an impossible event is zero (0).

   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 →
2. Q202 CBSE 2024
   Directions: A statement of Assertion (A) is followed by ​a ​statement ​of Reason ​(R). Choose the correct option.

   Assertion (A): The probability of getting number 8 on rolling a die is zero (0).

   Reason (R): The probability of an impossible event is zero (0).

   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 →
3. Q203 CBSE 2024
   Read ​the Assertion (A) and ​Reason ​(R) ​and choose the correct ​option.

   Assertion (A): The probability of getting an even number, when a die is thrown once, is $\frac{1}{2}$.

   Reason (R): In a die, total number of possible outcomes is $6$ and the even numbers are $2,4$ and $6$.

   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 →
4. Q204 CBSE 2024
   Assertion (A): In a cricket match, a batsman hits a boundary $9$ times out of $45$ balls he plays. The probability that in a given ball, he does not hit the boundary is $\frac{4}{5}$.

   Reason (R): $P(E)+P(\text{not }E)=1$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of 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 →
5. Q205 CBSE 2024
   Assertion (A): The probability ​of drawing a red face card, at random, from ​a well-shuffled pack of ​52 playing ​cards is $\frac{3}{26}$. Reason (R): The number of face cards ​in a pack of ​52 ​playing cards is ​16.

   Assertion (A): The probability of drawing a red face card, at random, from a well-shuffled pack of 52 playing cards is $\frac{3}{26}$.

   Reason (R): The number of face cards in a pack of 52 playing cards is 16.

   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

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

   Step-by-step solution →
6. Q206 CBSE 2024
   One card is ​drawn at random ​from a well ​shuffled deck of $52$ ​cards. Find the probability ​that the card ​drawn

   1. (i)is queen of hearts;
   2. (ii)is ​not a jack.
   Show answer

   (i) $P(\text{queen of hearts})=\frac{1}{52}$; (ii) $P(\text{not a jack})=\frac{12}{13}$

   Step-by-step solution →
7. Q207 CBSE 2024
   In a pack of $52$ playing cards ​one card is lost. From the remaining ​cards, a ​card ​is drawn at random. ​Find the probability that the ​drawn card is queen of heart, if the lost card is ​a black card.
   Show answer

   The required probability is $\frac{1}{51}$.

   Step-by-step solution →
8. Q208 CBSE 2024
   An ​integer is ​chosen at random from integers $1$ to $50$. ​Find the ​probability ​that ​the ​selected integer is divisible by $6$.
   Show answer

   The required probability is $\frac{4}{25}$ (that is, $\frac{8}{50}=0.16$).

   Step-by-step solution →
9. Q209 CBSE 2024
   $15$ defective ​pens are accidentally ​mixed with $145$ good ones. One pen ​is taken ​out at random from this ​lot. Determine ​the probability that the pen ​taken out ​is a good one.
   Show answer

   The probability that the pen taken out is a good one is $\frac{29}{32}$.

   Step-by-step solution →
10. Q210 CBSE 2024
    An unbiased ​die is ​thrown once. Find the probability ​of getting ​

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

    (i) $P(\text{number greater than }3)=\frac{1}{2}$; (ii) $P(\text{even prime number})=\frac{1}{6}$

    Step-by-step solution →
11. Q211 CBSE 2024
    A box contains 5 red, 8 white ​and 4 green marbles. ​One marble is drawn from the box at ​random. ​Find the probability ​of

    1. (i)getting a white marble
    2. (ii)not ​getting a green marble.
    Show answer

    (i) The probability of getting a white marble is $\frac{8}{17}$; (ii) The probability of not getting a green marble is $\frac{13}{17}$.

    Step-by-step solution →
12. Q212 CBSE 2024
    A ​bag contains $4$ red, $5$ white and some yellow ​balls. If probability ​of drawing a ​red ​ball at random is $\frac{1}{5}$, then find ​the probability of drawing a ​yellow ball at ​random.
    Show answer

    There are $11$ yellow balls out of $20$, so $P(\text{yellow})=\frac{11}{20}$.

    Step-by-step solution →
13. Q213 CBSE 2024
    A carton consists of $60$ shirts of which $48$ are good, $8$ ​have major defects and $4$ have minor defects. Nigam, a trader, will accept ​the shirts which are good but Anmol, another trader, will only reject the ​shirts which have major defects. One shirt is drawn at random from ​the carton. Find the ​probability that it ​is acceptable to ​Anmol.
    Show answer

    The probability that the shirt is acceptable to Anmol is $\frac{13}{15}$.

    Step-by-step solution →
14. Q214 CBSE 2024
    There are $80$ cards numbered ​from $1$ to $80$. ​One card ​is drawn ​at random ​from them. Find the probability ​that the number on the selected card is ​not divisible by $8$.
    Show answer

    The probability that the number on the card is not divisible by $8$ is $\frac{7}{8}$.

    Step-by-step solution →
15. Q215 CBSE 2024
    Two ​dice ​are ​tossed simultaneously. Find the probability of getting

    1. (a)an even number ​on both ​the ​dice,
    2. (b)​the ​sum of two numbers more than $9$.
    Show answer

    (a) $P(\text{both even})=\frac{9}{36}=\frac{1}{4}$; (b) $P(\text{sum}>9)=\frac{6}{36}=\frac{1}{6}$

    Step-by-step solution →
16. Q216 CBSE 2024
    Three coins are ​tossed ​simultaneously. ​What is the probability ​of getting

    1. (i)​at least one head ?
    2. (ii)exactly two ​tails ?
    3. (iii)​at most one tail ​?
    Show answer

    (i) $P(\text{at least one head})=\frac{7}{8}$; (ii) $P(\text{exactly two tails})=\frac{3}{8}$; (iii) $P(\text{at most one tail})=\frac{1}{2}$.

    Step-by-step solution →
17. Q217 CBSE 2024
    A box contains $90$ ​discs which are numbered $1$ to $90$. If one disc is drawn at random from the box, ​find the probability that it bears a :

    1. (i)2-digit number less than $40$.
    2. (ii)number divisible by $5$ and ​greater than $50$.
    3. (iii)​a ​perfect square number.
    Show answer

    (i) $P=\frac{1}{3}$; (ii) $P=\frac{4}{45}$; (iii) $P=\frac{1}{10}$

    Step-by-step solution →
18. Q218 CBSE 2024
    One card is drawn ​at random from ​a well-shuffled deck of 52 playing cards. ​Find the ​probability that the card drawn ​is :

    1. (i)a red ​king. ​
    2. (ii)not ​a black card.
    3. (iii)an ace of hearts.

    1. (i)a red king.[1]
    2. (ii)not a black card.[1]
    3. (iii)an ace of hearts.[1]
    Show answer

    (i) $P(\text{red king})=\frac{1}{26}$; (ii) $P(\text{not black})=\frac{1}{2}$; (iii) $P(\text{ace of hearts})=\frac{1}{52}$

    Step-by-step solution →
19. Q219 CBSE 2024
    Three ​unbiased ​coins ​are tossed simultaneously. Find the probability of getting :

    1. (i)at least ​one head.
    2. (ii)​exactly one tail.
    3. (iii)two heads ​and one tail.

    1. (i)at least one head.[1]
    2. (ii)exactly one tail.[1]
    3. (iii)two heads and one tail.[1]
    Show answer

    (i) $\frac{7}{8}$; (ii) $\frac{3}{8}$; (iii) $\frac{3}{8}$

    Step-by-step solution →
20. Q220 CBSE 2024
    The ​numbers ​on a die are replaced by the ​first six even ​numbers. The die is rolled once. ​Find the probability that the number appearing on the die is:

    1. (i)​greater than 4
    2. (ii)​divisible by 3
    3. (iii)not a multiple of 10.
    Show answer

    (i) $\frac{2}{3}$; (ii) $\frac{1}{3}$; (iii) $\frac{5}{6}$

    Step-by-step solution →