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 18 of 20

1. Q341 CBSE 2017
   All ​kings, ​jacks ​and diamonds have been removed from a pack of playing cards and the remaining cards are well-shuffled. A card is ​then drawn at random. Find the probability that ​the drawn card is a

   1. (i)face card.
   2. (ii)black ​card.

   1. (i)face card.
   2. (ii)black card.
   Show answer

   (i) $P(\text{face})=\frac{1}{11}$; (ii) $P(\text{black})=\frac{2}{3}$

   Step-by-step solution →
2. Q342 CBSE 2017
   A ​bag contains $12$ balls ​out of which some are white and the others ​are red. If the probability ​of drawing ​a white ​ball at random from the bag is $\frac{2}{3}$, then find how many ​red balls are there in the bag.
   Show answer

   There are $4$ red balls in the bag.

   Step-by-step solution →
3. Q343 CBSE 2017
   Two different dice ​are ​thrown together. Find ​the ​probability that the ​numbers obtained

   1. (i)​have a ​sum ​less than $7$
   2. (ii)have a product less than $16$
   3. (iii)is a doublet of odd numbers.

   1. (i)have a sum less than $7$
   2. (ii)have a product less than $16$
   3. (iii)is a doublet of odd numbers.
   Show answer

   (i) $P(\text{sum}<7)=\frac{15}{36}=\frac{5}{12}$; (ii) $P(\text{product}<16)=\frac{25}{36}$; (iii) $P(\text{odd doublet})=\frac{3}{36}=\frac{1}{12}$.

   Step-by-step solution →
4. Q344 CBSE 2017
   In a game, a one-rupee coin ​is tossed three ​times and the result is recorded every ​time. Haneef ​will ​win, if ​he ​gets at ​least two heads. Calculate Haneef's probability of losing the game.
   Show answer

   Haneef's probability of losing the game is $\frac{1}{2}$.

   Step-by-step solution →
5. Q345 CBSE 2017
   Two different dice are thrown together. ​Find ​the probability that ​the numbers obtained have

   1. (i)​even sum, ​and
   2. (ii)even ​product.

   1. ieven sum
   2. iieven product
   Show answer

   $P(\text{even sum})=\frac{1}{2}$ and $P(\text{even product})=\frac{3}{4}$.

   Step-by-step solution →
6. Q346 CBSE 2017
   A box contains $90$ discs ​which ​are numbered ​from $1$ to $90$. ​If one ​disc is ​drawn at random from the ​box, find the probability that it bears ​

   1. (i)a two-digit number,
   2. (ii)a number divisible by $5$.
   Show answer

   (i) $P(\text{two-digit})=\frac{9}{10}$; (ii) $P(\text{divisible by }5)=\frac{1}{5}$.

   Step-by-step solution →
7. Q347 CBSE 2017
   Two ​different ​dice are thrown at the same time. ​Find the probability that the numbers appearing ​on ​the ​two dice

   1. (i)​have a sum $8$. ​
   2. (ii)are first even and second odd.

   1. ihave a sum $8$.
   2. iiare first even and second odd.
   Show answer

   (i) $P(\text{sum}=8)=\frac{5}{36}$. (ii) $P(\text{first even, second odd})=\frac{1}{4}$.

   Step-by-step solution →
8. Q348 CBSE 2017
   Peter throws ​two different dice together and finds ​the product ​of ​the two ​numbers obtained. Rina throws a die and squares the number obtained. Who has ​the better chance to get ​the number $25$?
   Show answer

   $P(\text{Peter})=\frac{1}{36}$ and $P(\text{Rina})=\frac{1}{6}$. Since $\frac{1}{6}>\frac{1}{36}$, Rina has the better chance to get 25.

   Step-by-step solution →
9. Q349 CBSE 2017
   The king, ​the jack and the $10$ of spades are lost from a pack ​of $52$ cards and ​a ​card is drawn from the remaining cards after shuffling. Find the probability ​of getting a

   1. (i)red ​card,
   2. (ii)black jack,
   3. (iii)red king, ​and
   4. (iv)$10$ ​of hearts.

   1. (i)red card
   2. (ii)black jack
   3. (iii)red king
   4. (iv)10 of hearts
   Show answer

   (i) $\frac{26}{49}$, (ii) $\frac{1}{49}$, (iii) $\frac{2}{49}$, (iv) $\frac{1}{49}$.

   Step-by-step solution →
10. Q350 CBSE 2016
    A card ​is drawn ​at random from a well ​shuffled ​pack of $52$ playing ​cards. Find the probability of ​getting neither a red card ​nor a queen.
    Show answer

    $P(\text{neither red nor a queen})=\frac{6}{13}$.

    Step-by-step solution →
11. Q351 CBSE 2016
    A letter of English alphabets is ​chosen at ​random. Find ​the probability that the ​chosen letter is a ​letter ​of the word TRIGONOMETRY.
    Show answer

    $P(\text{letter in TRIGONOMETRY})=\frac{9}{26}$.

    Step-by-step solution →
12. Q352 CBSE 2016
    $20$ tickets, on which numbers $1$ to $20$ ​are written, are mixed thoroughly and then a ticket is drawn ​at random out of them. Find ​the probability ​that the number on the drawn ticket is a ​multiple of $3$ ​or $7$.
    Show answer

    $P(\text{multiple of }3\text{ or }7)=\frac{8}{20}=\frac{2}{5}$.

    Step-by-step solution →
13. Q353 CBSE 2016
    Cards marked ​with ​number $3,4,5,\dots ,50$ ​are placed in a box and mixed ​thoroughly. ​A card is ​drawn at random from the box. Find the probability that the selected card bears ​a perfect square number.
    Show answer

    The probability is $\frac{1}{8}$.

    Step-by-step solution →
14. Q354 CBSE 2016
    A ​letter of ​English alphabets is ​chosen at random. Find the probability that ​it is ​a ​letter of the word ​MATHEMATICS.
    Show answer

    $P(\text{letter of MATHEMATICS})=\frac{8}{26}=\frac{4}{13}$.

    Step-by-step solution →
15. Q355 CBSE 2016
    $15$ cards, ​numbered from $1$ to $15$ are put in ​a box and mixed thoroughly. ​Then ​a card is drawn at random from the box. Find the probability that the number ​on the drawn ​card is ​divisible by $2$ or $3$.
    Show answer

    Probability $=\frac{10}{15}=\frac{2}{3}$.

    Step-by-step solution →
16. Q356 CBSE 2016
    A coin is ​tossed $3$ times. ​Write ​all ​possible outcomes. Find the ​probability of getting at ​least $2$ ​heads.
    Show answer

    There are $8$ outcomes; $P(\text{at least 2 heads})=\frac{4}{8}=\frac{1}{2}$.

    Step-by-step solution →
17. Q357 CBSE 2016
    Black aces ​and black ​queens ​are removed ​from a ​pack of $52$ cards. Remaining cards are reshuffled and then a card is drawn. Find the ​probability of ​getting :

    1. (i)a black card
    2. (ii)an ace.

    1. ia black card
    2. iian ace
    Show answer

    (i) $P(\text{black card})=\frac{11}{24}$; (ii) $P(\text{ace})=\frac{1}{24}$.

    Step-by-step solution →
18. Q358 CBSE 2016
    There are $100$ ​cards in a bag on which ​numbers ​from $1$ to $100$ are written. A card is taken out from the bag at random. Find the probability that the number ​on ​the ​selected card

    1. (i)is divisible by $9$ and is a perfect ​square
    2. (ii)is a ​prime number greater than $80$.
    Show answer

    (i) $P=\frac{3}{100}$; (ii) $P=\frac{3}{100}$.

    Step-by-step solution →
19. Q359 CBSE 2016
    In a ​single throw of a pair of different dice, what is the probability ​of getting

    1. (i)​a ​prime number on ​each dice?
    2. (ii)​a ​total of $9$ or $11$?

    1. iProbability of getting a prime number on each dice.
    2. iiProbability of getting a total of $9$ or $11$.
    Show answer

    (i) $P(\text{prime on each})=\frac{1}{4}$; (ii) $P(\text{total }9\text{ or }11)=\frac{1}{6}$.

    Step-by-step solution →
20. Q360 CBSE 2016
    From a pack ​of $52$ playing cards, Jacks, Queens and Kings of red colour are removed. From the remaining, a ​card is drawn at random. Find the ​probability that ​drawn card is:

    1. (i)a black King ​
    2. (ii)a card of red colour
    3. (iii)a ​card of ​black colour.

    1. (i)a black King
    2. (ii)a card of red colour
    3. (iii)a card of black colour
    Show answer

    (i) $P(\text{black King})=\frac{1}{23}$; (ii) $P(\text{red})=\frac{10}{23}$; (iii) $P(\text{black})=\frac{13}{23}$.

    Step-by-step solution →