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 8 of 20

1. Q141 CBSE 2025
   A card ​is ​drawn at random from a deck ​of $52$ playing cards. ​The ​probability that ​the drawn ​card is not a red face card, is

   1. (a)$\frac{3}{26}$
   2. (b)$\frac{23}{26}$
   3. (c)$\frac{7}{52}$
   4. (d)$\frac{23}{52}$
   Show answer

   (b) $\frac{23}{26}$

   Step-by-step solution →
2. Q142 CBSE 2025
   Two ​dice ​are ​thrown at the same ​time. The probability ​that the ​sum appearing ​on the tops ​is $8$, is:

   1. (a)$\frac{5}{8}$
   2. (b)$\frac{5}{12}$
   3. (c)$\frac{5}{36}$
   4. (d)$\frac{1}{9}$
   Show answer

   (c) $\frac{5}{36}$

   Step-by-step solution →
3. Q143 CBSE 2025
   There is a square ​lawn ​of side 8 m inside a ​circular park of radius 20 m. Mr. Joseph wants ​to plant a sapling in the park. The probability that ​he can ​plant it outside the ​lawn is ​:

   1. (a)$\frac{32}{400\pi }$
   2. (b)$\frac{64}{400\pi }$
   3. (c)$\frac{400\pi -32}{400\pi }$
   4. (d)$\frac{400\pi -64}{400\pi }$
   Show answer

   (d) $\frac{400\pi -64}{400\pi }$

   Step-by-step solution →
4. Q144 CBSE 2025
   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 selecting a number at random from the numbers 1 to 20 is 1.

   Reason (R): For any event E, if $P(E)=1$, then E is called a sure event.

   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 →
5. Q145 CBSE 2025
   In an experiment ​of throwing a die, Assertion (A): ​Event $E_1$: getting a ​number less than $3$ and Event $E_2$: getting a ​number greater ​than $3$ are complementary ​events. Reason (R): If two events $E$ and $F$ are complementary ​events, then $P(E)+P(F)=1$.

   Assertion (A): In an experiment of throwing a die, Event $E_1$: getting a number less than $3$ and Event $E_2$: getting a number greater than $3$ are complementary events.

   Reason (R): If two events $E$ and $F$ are complementary events, then $P(E)+P(F)=1$.

   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

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

   Step-by-step solution →
6. Q146 CBSE 2025
   Two statements ​are ​given, one labelled as Assertion (A) and the other is labelled as ​Reason ​(R). ​Select the correct answer ​to these ​questions from the codes (a), (b), (c) and (d) as given below :

   Assertion (A): If E is an event such that $P(E)=\frac{1}{999}$, then $P(\overline{E})=0.001$.

   Reason (R): $P(E)+P(\overline{E})=1$

   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

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

   Step-by-step solution →
7. Q147 CBSE 2025
   The probability of ​guessing the correct answer of a certain test ​question is $\frac{x}{12}$. If ​the ​probability of not ​guessing the correct answer ​is $\frac{5}{6}$, then find the value of $x$.
   Show answer

   The value of $x$ is $2$.

   Step-by-step solution →
8. Q148 CBSE 2025
   From a pack of $52$ playing cards, jack, ​queen and king of diamonds ​are removed. A ​card is drawn at random from the remaining cards. Find ​the probability of getting a face card ​or ​a card ​of spades.
   Show answer

   The required probability is $\frac{19}{49}$.

   Step-by-step solution →
9. Q149 CBSE 2025
   Three ​different coins ​are tossed ​together. ​Find the probability of getting ​at least ​two ​tails.
   Show answer

   $P(\text{at least two tails})=\frac{1}{2}$

   Step-by-step solution →
10. Q150 CBSE 2025
    A ​box contains $120$ ​discs numbered from $1$ to $120$. One disc is drawn at random. Find the probability that

    1. (i)it ​bears a ​2-digit number,
    2. (ii)​the number is a perfect ​square.

    1. (i)
    2. (ii)
    Show answer

    (i) $P(\text{2-digit number})=\frac{90}{120}=\frac{3}{4}$; (ii) $P(\text{perfect square})=\frac{10}{120}=\frac{1}{12}$

    Step-by-step solution →
11. Q151 CBSE 2025
    A coin ​is dropped at random on the $3$ ​m by $2$ m ​rectangular region shown ​in the figure. ​What ​is the ​probability that it will land inside the circle with radius $0.7$ ​m?

    Show answer

    The required probability is $\frac{77}{300}$ (about $0.257$).

    Step-by-step solution →
12. Q152 CBSE 2025
    A ​die ​is thrown twice. ​What ​is ​the probability ​that

    1. (i)difference between two ​numbers obtained is $3$?
    2. (ii)​sum of the numbers obtained is $8$?
    Show answer

    (i) $P(\text{difference }3)=\frac{6}{36}=\frac{1}{6}$; (ii) $P(\text{sum }8)=\frac{5}{36}$

    Step-by-step solution →
13. Q153 CBSE 2025
    A bag contains ​40 ​marbles out of which some are ​white and others are ​black. If the ​probability of ​drawing a black marble is $\frac{3}{5}$, then ​find the ​number of white marbles.
    Show answer

    The number of white marbles is $16$.

    Step-by-step solution →
14. Q154 CBSE 2025
    A card ​is ​drawn at random from a pack ​of $50$ cards numbered $1$ to $50$. Find ​the ​probability ​of drawing a number ​which is a perfect square.
    Show answer

    The probability of drawing a perfect square is $\frac{7}{50}$.

    Step-by-step solution →
15. Q155 CBSE 2025
    A piggy bank contains ​fifty $\overline{\mathrm{R}}1$ coins, hundred $\overline{\mathrm{R}}2$ ​coins and ​one hundred and fifty $\overline{\mathrm{R}}5$ coins. If it is equally likely any one of the ​coins ​will fall out when the bank is turned upside down, find the probability that $\overline{\mathrm{R}}2$ coin has not fallen out, when ​the bank is turned upside down.
    Show answer

    The probability that a ₹2 coin has not fallen out is $\frac{2}{3}$.

    Step-by-step solution →
16. Q156 CBSE 2025
    In a ​pre-primary class, a teacher put cards ​numbered 20 ​to 59 in a bowl. A ​student ​picked up a card at random and read the number. Find the probability that the number read was ​

    1. (i)a prime number
    2. (ii)​a perfect square.
    Show answer

    (i) $P(\text{prime})=\frac{9}{40}$; (ii) $P(\text{perfect square})=\frac{3}{40}$

    Step-by-step solution →
17. Q157 CBSE 2025
    While ​shuffling a ​pack ​of 52 cards, one card ​was accidently ​dropped. Find the probability ​that the dropped card

    1. (i)is not a face card.
    2. (ii)​is ​a black king.
    Show answer

    (i) The probability that the dropped card is not a face card is $\frac{10}{13}$; (ii) The probability that it is a black king is $\frac{1}{26}$.

    Step-by-step solution →
18. Q158 CBSE 2025
    A die ​is thrown ​twice. Find ​the probability ​that $5$ will ​come up atleast ​once.
    Show answer

    The probability that $5$ comes up at least once is $\frac{11}{36}$.

    Step-by-step solution →
19. Q159 CBSE 2025
    Two friends ​Anil and Ashraf were born in the December ​month in the year $2010$. Find ​the probability that: ​

    1. (i)they share ​same date of ​birth.
    2. (ii)they ​have different dates of birth.
    Show answer

    (i) The probability that they share the same date of birth is $\frac{1}{31}$; (ii) The probability that they have different dates of birth is $\frac{30}{31}$.

    Step-by-step solution →
20. Q160 CBSE 2025
    The number of red balls ​in ​a ​bag is three more than the number ​of black balls. If the probability ​of drawing a ​red ball at random from the given ​bag is $\frac{12}{23}$, find the total number of ​balls in the given bag.
    Show answer

    The bag contains $33$ black and $36$ red balls, so the total number of balls in the bag is $69$.

    Step-by-step solution →