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 17 of 20

1. Q321 CBSE 2019
   A die ​is thrown once. Find the ​probability of getting

   1. (i)​a ​composite number, ​
   2. (ii)a prime number.

   1. ia composite number[1]
   2. iia prime number[1]
   Show answer

   (i) $P(\text{composite})=\frac{1}{3}$; (ii) $P(\text{prime})=\frac{1}{2}$

   Step-by-step solution →
2. Q322 CBSE 2019
   Cards marked with numbers $5$ to $50$ (one number on one card) are placed in ​a box and mixed thoroughly. ​One card is drawn at random from the box. Find the ​probability that the ​number on the card taken out is ​

   1. (i)a prime ​number less than $10$,
   2. (ii)a ​number which ​is a perfect square.
   Show answer

   (i) $\frac{1}{23}$;\ (ii) $\frac{5}{46}$

   Step-by-step solution →
3. Q323 CBSE 2019
   A die ​is thrown ​once. Find the probability of getting ​a number ​which

   1. (i)​is a ​prime number
   2. (ii)lies between $2$ and $6$.

   1. (i)is a prime number
   2. (ii)lies between 2 and 6
   Show answer

   (i) $P(\text{prime})=\frac{1}{2}$; (ii) $P(\text{between 2 and 6})=\frac{1}{2}$.

   Step-by-step solution →
4. Q324 CBSE 2019
   $12$ defective pens are accidentally mixed up with $132$ good ones. It ​is not possible ​to just look at a pen and tell whether it ​is defective or not. One pen ​is taken out at ​random from the lot. Find ​the probability that the pen taken out ​is a good ​one.
   Show answer

   $P(\text{good pen})=\frac{132}{144}=\frac{11}{12}$.

   Step-by-step solution →
5. Q325 CBSE 2019
   Cards ​numbered $7$ ​to $40$ were put ​in ​a box. ​Poonam selects a card at ​random. ​What is the probability that ​Poonam selects a card which is a multiple of $7$?
   Show answer

   $P(\text{multiple of }7)=\frac{5}{34}$

   Step-by-step solution →
6. Q326 CBSE 2018
   A ​bag contains $5$ red balls ​and some blue balls. ​If the ​probability of drawing ​a blue ball from the bag is three times that of a red ball, find ​the ​number of blue ​balls in the bag.
   Show answer

   There are $15$ blue balls in the bag.

   Step-by-step solution →
7. Q327 CBSE 2018
   Two different dice are tossed together. Find the probability ​: ​

   1. (i)​of getting ​a doublet
   2. (ii)​of ​getting ​a sum $10$, of the numbers on the two ​dice.

   1. iof getting a doublet
   2. iiof getting a sum 10, of the numbers on the two dice
   Show answer

   (i) $P(\text{doublet})=\frac{1}{6}$; (ii) $P(\text{sum}=10)=\frac{1}{12}$.

   Step-by-step solution →
8. Q328 CBSE 2018
   Two different dice are ​tossed together. ​Find ​the probability:

   1. (i)​of getting a doublet
   2. (ii)of getting a ​sum 10, of the numbers on ​the two dice.

   1. (i)of getting a doublet
   2. (ii)of getting a sum 10, of the numbers on the two dice
   Show answer

   (i) $P(\text{doublet})=\frac{1}{6}$; (ii) $P(\text{sum}=10)=\frac{1}{12}$

   Step-by-step solution →
9. Q329 CBSE 2018
   A card is ​drawn at random from a well ​shuffled pack of $52$ ​playing cards. Find the probability of getting ​

   1. (i)a red ​king
   2. (ii)a ​queen ​or a jack.

   1. ia red king
   2. iia queen or a jack
   Show answer

   (i) $P(\text{red king})=\frac{1}{26}$; (ii) $P(\text{queen or jack})=\frac{2}{13}$.

   Step-by-step solution →
10. Q330 CBSE 2018
    An ​integer is chosen ​at random between $1$ ​and $100$. ​Find the probability that it ​is :

    1. (i)divisible ​by $8$.
    2. (ii)not divisible by $8$.

    1. (i)divisible by $8$.
    2. (ii)not divisible by $8$.
    Show answer

    (i) $P=\frac{6}{49}$; (ii) $P=\frac{43}{49}$.

    Step-by-step solution →
11. Q331 CBSE 2017
    The probability of selecting a rotten apple ​randomly from ​a heap of ​900 apples ​is $0.18$. What is ​the number of rotten apples in the ​heap?
    Show answer

    There are $162$ rotten apples.

    Step-by-step solution →
12. Q332 CBSE 2017
    The probability of selecting a ​rotten ​apple randomly from ​a heap ​of $900$ ​apples is $0.18$. What ​is the ​number ​of rotten apples in the heap?
    Show answer

    The number of rotten apples is $162$.

    Step-by-step solution →
13. Q333 CBSE 2017
    A number is selected ​at random from natural ​numbers $1$ to $20$. Find ​the probability ​that the selected ​number is ​a prime ​number.
    Show answer

    $P(\text{prime})=\frac{8}{20}=\frac{2}{5}$.

    Step-by-step solution →
14. Q334 CBSE 2017
    A number ​is chosen at random ​from ​the numbers $-3,-2,-1,0,1,2,3$. ​What will be the ​probability ​that square of this number is less than or equal ​to $1$?
    Show answer

    The probability that the square of the chosen number is $\le 1$ is $\frac{3}{7}$.

    Step-by-step solution →
15. Q335 CBSE 2017
    Find the ​probability of getting the ​sum ​of ​two numbers, less than $3$ or more than $11$ when a pair ​of ​distinct ​dice is ​thrown together.
    Show answer

    The required probability is $\frac{2}{36}=\frac{1}{18}$.

    Step-by-step solution →
16. Q336 CBSE 2017
    Two ​different dice are ​thrown together. Find the probability that the ​product of the ​numbers appeared ​is ​less than $18$.
    Show answer

    $P(\text{product}<18)=\frac{26}{36}=\frac{13}{18}$.

    Step-by-step solution →
17. Q337 CBSE 2017
    $20$ ​cards, numbered from $11$ to $30$, are put in a box and ​mixed thoroughly. A card is then drawn from the box at random. Find the probability ​that ​the ​number ​on ​the drawn card is a prime number.
    Show answer

    $P(\text{prime})=\frac{3}{10}$

    Step-by-step solution →
18. Q338 CBSE 2017
    Find ​the probability that in a leap ​year there ​will ​be $53$ ​Tuesdays.
    Show answer

    $P(53\text{ Tuesdays})=\frac{2}{7}$.

    Step-by-step solution →
19. Q339 CBSE 2017
    A bag contains ​15 white and ​some black balls. If ​the probability of drawing a black ball from the bag ​is thrice that of drawing a white ball, find the ​number of black balls in ​the ​bag.
    Show answer

    There are $45$ black balls in the bag.

    Step-by-step solution →
20. Q340 CBSE 2017
    A bag contains $15$ ​white and ​some black balls. If the probability of drawing a black ball ​from the bag is thrice that ​of drawing a white ​ball, ​find ​the number of black balls in the bag.
    Show answer

    There are $45$ black balls in the bag.

    Step-by-step solution →