Class 10 Maths · Chapter 14

Probability

89 Class 10 Maths questions on Probability from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 5

1. Q21 NCERT · Exercise 14.1
   A lot consists of 144 ​ball ​pens of which ​20 are defective and the others are good. Nuri will buy ​a pen if it is good, but will not buy if ​it is defective. The ​shopkeeper draws one pen at random and gives it to her. ​What is the probability that

   1. (i)She will buy it?
   2. (ii)She will not ​buy it?
   Show answer

   (i) $P(\text{she will buy})=\frac{31}{36}$; (ii) $P(\text{she will not buy})=\frac{5}{36}$.

   Step-by-step solution →
2. Q22 NCERT · Exercise 14.1
   Refer ​to Example ​13.

   1. (i)Complete ​the following table giving the probability ​for each possible sum when two dice are ​thrown together. Some entries are filled in to help you.
   2. (ii)A student argues that there are 11 possible outcomes 2, 3, 4, 5, ​6, 7, ​8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify ​your answer.

   Sum on 2 dice and its probability (entries to be completed in part (i))

   Event: Sum on 2 dice	2	3	4	5	6	7	8	9	10	11	12
   Probability	$\frac{1}{36}$						$\frac{5}{36}$				$\frac{1}{36}$

   Show answer

   (i) $P(\text{sum})$ for $2,3,\dots ,12$ is $\frac{1}{36},\frac{2}{36},\frac{3}{36},\frac{4}{36},\frac{5}{36},\frac{6}{36},\frac{5}{36},\frac{4}{36},\frac{3}{36},\frac{2}{36},\frac{1}{36}$. (ii) No. The $11$ sums are not equally likely (e.g. $P(7)=\frac{6}{36}$ but $P(2)=\frac{1}{36}$), so each is not $\frac{1}{11}$.

   Step-by-step solution →
3. Q23 NCERT · Exercise 14.1
   A game consists of tossing a one rupee coin 3 times and ​noting ​its outcome each time. Hanif wins if ​all the tosses give the same result ​i.e., ​three heads or three tails, and loses otherwise. Calculate the ​probability that Hanif will lose the ​game.
   Show answer

   $P(\text{Hanif loses})=\frac{3}{4}=0.75$.

   Step-by-step solution →
4. Q24 NCERT · Exercise 14.1
   A die is thrown ​twice. What is the probability that

   1. (i)$5$ ​will ​not come ​up either time?
   2. (ii)$5$ ​will come up at least once? ​[Hint: Throwing a die twice and throwing two dice simultaneously are treated as ​the same experiment.]
   Show answer

   (i) $P(\text{no }5)=\frac{25}{36}$; (ii) $P(\text{at least one }5)=\frac{11}{36}$.

   Step-by-step solution →
5. Q25 NCERT · Exercise 14.1
   Which of the following arguments are correct and which are ​not correct? Give ​reasons for your answer.

   1. (i)If ​two coins are tossed simultaneously there are three possible outcomes - two heads, two tails or one of each. Therefore, for each of ​these outcomes, ​the probability is $\frac{1}{3}$.
   2. (ii)If a die is thrown, there are two possible outcomes - an odd number or an even number. Therefore, the probability ​of getting an odd number ​is $\frac{1}{2}$.
   Show answer

   (i) Not correct — the three outcomes are not equally likely ('one of each' covers HT and TH, so $P=\frac{1}{4},\frac{1}{4},\frac{1}{2}$, not $\frac{1}{3}$ each). (ii) Correct — three of the six faces are odd, so $P(\text{odd})=\frac{1}{2}$.

   Step-by-step solution →
6. Q26 Exemplar · Exercise 13.1
   If an ​event cannot ​occur, ​then its ​probability is

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

   (d) 0

   Step-by-step solution →
7. Q27 Exemplar · Exercise 13.1
   Which of ​the following cannot ​be the ​probability ​of ​an ​event?

   1. (a)$\frac{1}{3}$
   2. (b)$0.1$
   3. (c)$3\%$
   4. (d)$\frac{17}{16}$
   Show answer

   (d) $\frac{17}{16}$

   Step-by-step solution →
8. Q28 Exemplar · Exercise 13.1
   An ​event ​is very unlikely to happen. ​Its probability ​is ​closest ​to

   1. (a)0.0001
   2. (b)0.001
   3. (c)0.01
   4. (d)0.1
   Show answer

   (a) 0.0001

   Step-by-step solution →
9. Q29 Exemplar · Exercise 13.1
   If the probability ​of ​an ​event ​is $p$, ​the probability ​of its ​complementary event will be

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

   (c) $1-p$

   Step-by-step solution →
10. Q30 Exemplar · Exercise 13.1
    The probability expressed as a percentage of ​a ​particular occurrence ​can ​never ​be

    1. (a)less than 100
    2. (b)less than 0
    3. (c)greater than 1
    4. (d)anything but a whole number
    Show answer

    (b) less than 0

    Step-by-step solution →
11. Q31 Exemplar · Exercise 13.1
    If $P(A)$ denotes ​the ​probability ​of an ​event $A$, then

    1. (a)$P(A)<0$
    2. (b)$P(A)>1$
    3. (c)$0\le P(A)\le 1$
    4. (d)$-1\le P(A)\le 1$
    Show answer

    (c) $0\le P(A)\le 1$

    Step-by-step solution →
12. Q32 Exemplar · Exercise 13.1
    A card is ​selected from ​a deck of ​52 ​cards. ​The probability of ​its being a ​red face card ​is

    1. (a)$\frac{3}{26}$
    2. (b)$\frac{3}{13}$
    3. (c)$\frac{2}{13}$
    4. (d)$\frac{1}{2}$
    Show answer

    (a) $\frac{3}{26}$

    Step-by-step solution →
13. Q33 Exemplar · Exercise 13.1
    The probability ​that a ​non leap year ​selected at ​random will contain ​53 Sundays is

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

    (a) $\frac{1}{7}$

    Step-by-step solution →
14. Q34 Exemplar · Exercise 13.1
    When ​a die is ​thrown, ​the probability of ​getting ​an ​odd number ​less than $3$ is

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

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

    Step-by-step solution →
15. Q35 Exemplar · Exercise 13.1
    A card is drawn ​from a ​deck of 52 ​cards. The event ​E is that card is ​not ​an ​ace of hearts. The number of outcomes favourable to E ​is

    1. (a)$4$
    2. (b)$13$
    3. (c)$48$
    4. (d)$51$
    Show answer

    (d) $51$

    Step-by-step solution →
16. Q36 Exemplar · Exercise 13.1
    The probability of ​getting a bad ​egg ​in a lot of 400 is ​0.035. The number of bad eggs ​in the ​lot is

    1. (a)$7$
    2. (b)$14$
    3. (c)$21$
    4. (d)$28$
    Show answer

    (b) $14$

    Step-by-step solution →
17. Q37 Exemplar · Exercise 13.1
    A girl calculates that the probability of her winning the ​first prize in ​a ​lottery is $0.08$. If $6000$ ​tickets ​are sold, how many tickets has ​she bought?

    1. (a)$40$
    2. (b)$240$
    3. (c)$480$
    4. (d)$750$
    Show answer

    (c) $480$

    Step-by-step solution →
18. Q38 Exemplar · Exercise 13.1
    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 5 is

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

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

    Step-by-step solution →
19. Q39 Exemplar · Exercise 13.1
    Someone is ​asked to ​take a ​number ​from ​1 to 100. The probability that it is a ​prime ​is

    1. (a)$\frac{1}{5}$
    2. (b)$\frac{6}{25}$
    3. (c)$\frac{1}{4}$
    4. (d)$\frac{13}{50}$
    Show answer

    (c) $\frac{1}{4}$

    Step-by-step solution →
20. Q40 Exemplar · Exercise 13.1
    A ​school has five houses A, B, C, D and E. ​A class has ​23 students, 4 from house A, 8 ​from house B, 5 from house C, 2 from house D and rest from ​house E. A single student is ​selected at random to be the class monitor. The ​probability that the selected student is not ​from A, B and C is

    1. (a)$\frac{4}{23}$
    2. (b)$\frac{6}{23}$
    3. (c)$\frac{8}{23}$
    4. (d)$\frac{17}{23}$
    Show answer

    (b) $\frac{6}{23}$

    Step-by-step solution →