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 9 of 20

1. Q161 CBSE 2025
   Three unbiased coins are tossed simultaneously. Find ​the probability of getting :

   1. (a)exactly ​two ​tails
   2. (b)at least ​one ​head
   3. (c)at most two heads
   Show answer

   (a) The probability of exactly two tails is $\frac{3}{8}$; (b) The probability of at least one head is $\frac{7}{8}$; (c) The probability of at most two heads is $\frac{7}{8}$.

   Step-by-step solution →
2. Q162 CBSE 2025
   A ​box contains $6$ blue, $4$ white and $8$ red marbles. A marble is drawn at random ​from this ​box. Find the probability that the marble ​so drawn is:

   1. (i)white
   2. (ii)​white ​or ​red
   3. (iii)not red
   Show answer

   (i) $P(\text{white})=\frac{2}{9}$; (ii) $P(\text{white or red})=\frac{2}{3}$; (iii) $P(\text{not red})=\frac{5}{9}$

   Step-by-step solution →
3. Q163 CBSE 2025
   A game ​of ​chance consists of spinning a wheel which comes to rest at one of the numbers from 1 to 10 (as shown in the given figure) with equal ​probabilities. What is the probability that the wheel stops at

   1. (i)a prime number ​greater than 2 ​?
   2. (ii)​an odd number less than 9 ​?
   3. (iii)a multiple of ​4 ?

   Show answer

   (i) $\frac{3}{10}$; (ii) $\frac{2}{5}$; (iii) $\frac{1}{5}$

   Step-by-step solution →
4. Q164 CBSE 2025
   Two ​dice ​are ​thrown ​at the same time. Determine the ​probability ​that the ​difference ​of the numbers on the two dice is 2.
   Show answer

   There are $8$ favourable outcomes out of $36$, so the probability that the numbers on the two dice differ by $2$ is $\frac{8}{36}=\frac{2}{9}$.

   Step-by-step solution →
5. Q165 CBSE 2025
   All jacks, queens ​and kings are removed from a pack of $52$ ​playing cards. The remaining ​cards are ​well shuffled and then a ​card is drawn at random from these remaining cards. Find the probability that this card is:

   1. (i)a black face card
   2. (ii)a ​red ​card
   3. (iii)a black ace card
   Show answer

   (i) $P(\text{black face card})=0$; (ii) $P(\text{red card})=\frac{1}{2}$; (iii) $P(\text{black ace})=\frac{1}{20}$

   Step-by-step solution →
6. Q166 CBSE 2025
   A lot consists of 200 pens of which ​180 are ​good and the rest are ​defective. A customer will ​buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is ​the ​probability that the customer will not buy it? Another lot of 100 pens containing ​80 good pens ​is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen?
   Show answer

   The probability that the customer will not buy the pen from the first lot is $\frac{1}{10}$; the probability that the customer will buy the pen from the mixed lot is $\frac{13}{15}$.

   Step-by-step solution →
7. Q167 CBSE 2025
   Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from $10$ to $74$. Before ​each match, he draws a card from the jar. ​If the card bears an even number, the team wins. If the number is even ​and divisible by $5$, they win by a big margin. If the number is an odd number less than $30$, they win by a ​small margin. And ​if the number is a prime number ​between $50$ and $74$, they lose. Answer the following questions if Rahul draws a card today :

   1. (i)What is the probability that Rahul draws a card with an even number?[1]
   2. (ii)What is the probability that Rahul draws a card with an odd number less than $30$?[1]
   3. (iii)(a)What is the probability that Rahul draws a card with a prime number between $50$ and $74$?[2]
   4. (iii)(b) [OR]What is the probability that Rahul draws a card with an even number divisible by $5$?[2]
   Show answer

   (i) $P(\text{even number})=\frac{33}{65}$; (ii) $P(\text{odd number less than }30)=\frac{10}{65}=\frac{2}{13}$; (iii)(a) $P(\text{prime number between }50\text{ and }74)=\frac{6}{65}$; (iii)(b) $P(\text{even number divisible by }5)=\frac{7}{65}$.

   Step-by-step solution →
8. Q168 CBSE 2025
   Aarav and Ashima are brother ​and sister and on Ashima's birthday, Aarav ​gifts her a bag filled with $8$ red ​toffees, $10$ green toffees and $6$ blue toffees. ​Ashima decides to randomly draw ​a toffee from ​the bag. She wants ​to find the chances of picking a toffee of specific colour and asks the ​following questions :

   1. (i)What is the probability of getting a green toffee?[1]
   2. (ii)What is the probability of getting a blue toffee?[1]
   3. (iii)(a)What is the probability of getting a non-red toffee?[2]
   4. (iii)(b)What is the probability of getting a red or a green toffee? (OR alternative to (iii)(a))[2]
   Show answer

   (i) $P(\text{green})=\frac{5}{12}$; (ii) $P(\text{blue})=\frac{1}{4}$; (iii)(a) $P(\text{non-red})=\frac{2}{3}$; (iii)(b) $P(\text{red or green})=\frac{3}{4}$

   Step-by-step solution →
9. Q169 CBSE 2024
   If the ​probability of a player winning ​a ​game is $0.79$, then the probability of ​his ​losing ​the same game is :

   1. (a)$1.79$
   2. (b)$0.31$
   3. (c)$0.21\%$
   4. (d)$0.21$
   Show answer

   (d) $0.21$

   Step-by-step solution →
10. Q170 CBSE 2024
    Two ​dice ​are thrown ​together. ​The ​probability that they show different ​numbers is :

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

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

    Step-by-step solution →
11. Q171 CBSE 2024
    Which ​of ​the following ​relationship ​is correct ?

    1. (a)$P(E)=1+P(\overline{E})$
    2. (b)$P(\overline{E})-P(E)=1$
    3. (c)$P(E)+P(\overline{E})=1$
    4. (d)$P(E)=2P(\overline{E})$
    Show answer

    (c) $P(E)+P(\overline{E})=1$

    Step-by-step solution →
12. Q172 CBSE 2024
    A die is rolled ​once. What is ​the probability ​of getting an ​odd prime ​number ?

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

    (b) 1/3

    Step-by-step solution →
13. Q173 CBSE 2024
    The probability of guessing ​the ​correct answer to a certain ​test question ​is $\frac{x}{6}$. If the probability of not guessing the ​correct answer to this question is $\frac{2}{3}$, then ​the value ​of $x$ is :

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

    (a) 2

    Step-by-step solution →
14. Q174 CBSE 2024
    The probability ​of getting ​a ​sum ​of 8, when ​two dice are thrown simultaneously, is ​:

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

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

    Step-by-step solution →
15. Q175 CBSE 2024
    One ​ticket is drawn at random ​from a bag containing ​tickets numbered $1$ to $40$. ​The probability that the selected ticket has a number which ​is a ​multiple of $7$ is :

    1. (a)$\frac{1}{7}$
    2. (b)$\frac{1}{8}$
    3. (c)$\frac{1}{5}$
    4. (d)$\frac{7}{40}$
    Show answer

    (b) $\frac{1}{8}$

    Step-by-step solution →
16. Q176 CBSE 2024
    If ​probability ​of ​winning a game ​is $p$, then ​probability of ​losing the game is:

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

    (d) $1-p$

    Step-by-step solution →
17. Q177 CBSE 2024
    All queens, jacks and aces are removed from a pack of 52 playing ​cards. The remaining ​cards are well-shuffled ​and one ​card is picked up ​at random from ​it. The probability of ​that card to be a king is :

    1. (a)$\frac{1}{10}$
    2. (b)$\frac{1}{13}$
    3. (c)$\frac{3}{10}$
    4. (d)$\frac{3}{13}$
    Show answer

    (a) $\frac{1}{10}$

    Step-by-step solution →
18. Q178 CBSE 2024
    Two dice are ​rolled together. The probability of getting ​the sum ​of ​the ​two numbers to ​be more ​than $10$, ​is

    1. (a)$\frac{1}{9}$
    2. (b)$\frac{1}{6}$
    3. (c)$\frac{7}{12}$
    4. (d)$\frac{1}{12}$
    Show answer

    (d) $\frac{1}{12}$

    Step-by-step solution →
19. Q179 CBSE 2024
    From the ​data $1,4,7,9,16,21,25$, if all the even ​numbers are removed, ​then ​the probability ​of getting at random a prime ​number from the remaining ​is :

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

    (b) $\frac{1}{5}$

    Step-by-step solution →
20. Q180 CBSE 2024
    A ​die is thrown once. The ​probability ​of ​getting a number ​less than ​6, ​is :

    1. (a)$0$
    2. (b)$\frac{5}{6}$
    3. (c)$\frac{1}{6}$
    4. (d)$1$
    Show answer

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

    Step-by-step solution →