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 6 of 20

1. Q101 CBSE 2026
   Find the probability ​that ​a number ​selected at random ​from ​the numbers $30,31,32,33,\dots ,60$ is

   1. (i)a prime number
   2. (ii)​a multiple ​of $6$.
   Show answer

   (i) $P(\text{prime})=\frac{7}{31}$; (ii) $P(\text{multiple of }6)=\frac{6}{31}$.

   Step-by-step solution →
2. Q102 CBSE 2026
   Slips ​of letters ​of the word 'BACKGROUND' ​are ​put in a bowl and thoroughly mixed. One slip is picked up ​at random. Find the probability that picked up slip's letter ​is

   1. (i)a ​vowel
   2. (ii)present in the word 'BALL'.
   Show answer

   (i) The probability of a vowel is $\frac{3}{10}$. (ii) The probability the letter is present in 'BALL' is $\frac{2}{10}=\frac{1}{5}$.

   Step-by-step solution →
3. Q103 CBSE 2026
   All ​the red face cards ​are removed from a pack of $52$ playing cards. The ​remaining cards are well shuffled ​and then ​a card is ​drawn at random. Find the probability of getting a:

   1. (i)​red card
   2. (ii)​a king or queen
   Show answer

   (i) $P(\text{red card})=\frac{10}{23}$; (ii) $P(\text{king or queen})=\frac{2}{23}$.

   Step-by-step solution →
4. Q104 CBSE 2026
   A ​bag ​contains $25$ balls. ​Some of them are yellow ​and others are green. ​One ball ​is drawn at random. If probability of getting a green ball is $\frac{3}{5}$, then find the ​number of yellow balls.
   Show answer

   The number of yellow balls is $10$.

   Step-by-step solution →
5. Q105 CBSE 2026
   A box consists of $60$ wall clocks, out of which $40$ ​are good, $15$ have minor defects and the remaining ​are broken. A ​trader will reject the ​box, if the clock taken out from the box is broken. The trader randomly ​takes out one clock from the box. ​What is the probability that :

   1. (i)the box will be rejected ?
   2. (ii)the clock taken out of the ​box has minor ​defect ?
   Show answer

   (i) The probability that the box will be rejected is $\frac{5}{60}=\frac{1}{12}$; (ii) The probability that the clock taken out has a minor defect is $\frac{15}{60}=\frac{1}{4}$.

   Step-by-step solution →
6. Q106 CBSE 2026
   A square ​dart board is divided into four equal squares as shown in the figure given below. ​If a dart hits square $APOS$, a player wins ₹ $100$. If a dart hits square $BPOQ$, a player ​loses ₹ $50$. If a dart hits square $OQCR$, a player loses ₹ $100$ and if it hits square $ORDS$, the player will win ₹ $25$. A ​player takes a turn and ​hits the dart ​board. What is the probability that

   1. (i)the ​player loses money ?
   2. (ii)the player wins ₹ $100$ ?

   Show answer

   (i) P(the player loses money) $=\frac{2}{4}=\frac{1}{2}$; (ii) P(the player wins ₹ $100$) $=\frac{1}{4}$

   Step-by-step solution →
7. Q107 CBSE 2026
   A game of ​chance consists of spinning an arrow which ​comes to rest in one of the six equal ​sectors as shown in the ​given figure. A person ​spins an arrow once. What is the ​probability ​that the person

   1. (i)wins a laptop ?
   2. (ii)​does not get a chance to spin again ?

   Show answer

   (i) P(wins a laptop) $=\frac{1}{6}$; (ii) P(does not get a chance to spin again) $=\frac{5}{6}$.

   Step-by-step solution →
8. Q108 CBSE 2026
   A bag contains $30$ ​balls out ​of ​which '$m$' number of balls are blue in colour.

   1. (i)Find the probability that ​a ball drawn ​at random from the bag is not blue.
   2. (ii)If $6$ more blue ​balls are added in the bag, then the probability of drawing a blue ball will ​be $\frac{5}{4}$ times the probability of drawing a blue ball in the first case. Find the value ​of $m$.
   Show answer

   (i) $P(\text{not blue})=\frac{30-m}{30}$ (with $m=12$ from part (ii), this equals $\frac{18}{30}=\frac{3}{5}$); (ii) $m=12$.

   Step-by-step solution →
9. Q109 CBSE 2026
   Two dice are ​rolled together. ​Find the probability that: ​

   1. (i)the ​sum of the numbers obtained is $10$. ​
   2. (ii)the product of ​the ​numbers obtained is $6$.
   Show answer

   (i) $P(\text{sum}=10)=\frac{1}{12}$; (ii) $P(\text{product}=6)=\frac{1}{9}$.

   Step-by-step solution →
10. Q110 CBSE 2026
    Two dice of different colours are thrown at the same ​time. ​Write down all ​the possible ​outcomes. What is the ​probability that :

    1. (i)​same number ​appears on both ​the dice ?
    2. (ii)different number appears on both the dice ?
    Show answer

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

    Step-by-step solution →
11. Q111 CBSE 2026
    Two dice are thrown at the ​same time. Determine ​the probability that ​the

    1. (i)sum of the ​numbers ​on the two dice ​is $5$, and
    2. (ii)difference of the ​numbers on the two dice is $3$.
    Show answer

    (i) The probability that the sum of the numbers is $5$ is $\frac{1}{9}$; (ii) The probability that the difference of the numbers is $3$ is $\frac{1}{6}$.

    Step-by-step solution →
12. Q112 CBSE 2026
    A group of friends ​wanted to play cards with two identical packs together. While shuffling ​the cards, three ​cards are dropped. Rest of the cards are ​shuffled and one ​card is drawn at ​random. Assuming that the dropped cards were a ​queen of hearts, a ten of spades and an ace of clubs, answer the following questions :

    1. (i)Find the probability that the drawn card is a face card.[1]
    2. (ii)Find the probability that the drawn card is either a king or a queen.[1]
    3. (iii)(a)Do you think that the probability of getting a queen was higher if none of the cards were dropped ? Justify your answer.[2]
    4. (iii)(b)OR : Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher ?[2]
    Show answer

    (i) $P(\text{face card})=\frac{23}{101}$; (ii) $P(\text{king or queen})=\frac{15}{101}$; (iii)(a) Yes — a queen was more likely before the drop, since $\frac{8}{104}=\frac{1}{13}\approx 0.077$ is greater than $\frac{7}{101}\approx 0.069$; (iii)(b) $P(\text{jack})=\frac{8}{101}$ now versus $\frac{8}{104}=\frac{1}{13}$ if none were dropped, so the jack is more likely after the drop.

    Step-by-step solution →
13. Q113 CBSE 2026
    Raghav has a collection of balls ​of different ​colours. He has a ​total of $35$ balls ​in his basket, out of which ​seven are black and eight are yellow. Out of the remaining balls, ​some are white and the rest are red.

    1. (a)If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket.[2]
    2. (b)Find the probability of drawing a ball at random from the basket which is either a black or a white ball.[2]
    Show answer

    (a) The number of red balls is $15$ (with $5$ white balls). (b) $P(\text{black or white})=\frac{12}{35}$.

    Step-by-step solution →
14. Q114 CBSE 2025
    The ​probability ​of drawing ​an ​even prime number out ​of numbers from $1$ ​to $30$ ​is ​:

    1. (a)$\frac{1}{30}$
    2. (b)$\frac{4}{15}$
    3. (c)$\frac{7}{30}$
    4. (d)$0$
    Show answer

    (a) $\frac{1}{30}$

    Step-by-step solution →
15. Q115 CBSE 2025
    Two ​different coins are ​tossed together. ​The probability of getting exactly one ​tail ​is :

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

    (b) $\frac{1}{2}$

    Step-by-step solution →
16. Q116 CBSE 2025
    Three ​coins ​are ​tossed together. ​The probability that only one coin shows tail, is ​:

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

    (b) $\frac{3}{8}$

    Step-by-step solution →
17. Q117 CBSE 2025
    The number ​of ​red ​balls ​in ​a bag is $10$ ​more than the number of black balls. If the probability of drawing a red ball at random from ​this bag is $\frac{3}{5}$, then the ​total number of balls in the bag is:

    1. (a)$50$
    2. (b)$60$
    3. (c)$80$
    4. (d)$40$
    Show answer

    (a) $50$

    Step-by-step solution →
18. Q118 CBSE 2025
    Two dice ​are rolled ​together. ​The ​probability of getting a sum ​more ​than $9$ ​is

    1. (a)$\frac{5}{6}$
    2. (b)$\frac{5}{18}$
    3. (c)$\frac{1}{6}$
    4. (d)$\frac{1}{2}$
    Show answer

    (c) $\frac{1}{6}$

    Step-by-step solution →
19. Q119 CBSE 2025
    Cards numbered $10,11,12,\dots ,30$ are kept in a box ​and shuffled ​thoroughly. ​Rohit draws a ​card at ​random from the box. The probability that the number on the card is ​a ​multiple of 4 or 5 is :

    1. (a)$\frac{9}{20}$
    2. (b)$\frac{9}{21}$
    3. (c)$\frac{10}{20}$
    4. (d)$\frac{10}{21}$
    Show answer

    (b) $\frac{9}{21}$

    Step-by-step solution →
20. Q120 CBSE 2025
    A bag ​contains ​red balls ​and black ​balls in the ratio $3:7$. A ball is ​drawn at random. The ​probability that ball so ​drawn ​is black in colour, is

    1. (a)$\frac{3}{7}$
    2. (b)$0.3$
    3. (c)$0.7$
    4. (d)$\frac{1}{7}$
    Show answer

    (c) $0.7$

    Step-by-step solution →