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 3 of 5

1. Q41 Exemplar · Exercise 13.2
   In a family having three children, ​there may ​be no girl, one girl, two ​girls or ​three girls. So, the ​probability of each ​is $\frac{1}{4}$. ​Is this correct? Justify your answer.
   Show answer

   No, it is not correct. The four events are not equally likely; $P(0)=\frac{1}{8}$, $P(1)=\frac{3}{8}$, $P(2)=\frac{3}{8}$, $P(3)=\frac{1}{8}$.

   Step-by-step solution →
2. Q42 Exemplar · Exercise 13.2
   A game consists of spinning an ​arrow which ​comes to rest ​pointing at ​one of the regions (1, ​2 or 3) (Fig. 13.1). Are the ​outcomes 1, 2 and 3 equally ​likely to occur? ​Give reasons.

   Show answer

   No. Regions 1 and 2 are quarter-circles ($P=\frac{1}{4}$ each) while region 3 is a semicircle ($P=\frac{1}{2}$), so outcome 3 is twice as likely; the outcomes are not equally likely.

   Step-by-step solution →
3. Q43 Exemplar · Exercise 13.2
   Apoorv throws two ​dice once and computes the product of the numbers ​appearing on the ​dice. Peehu throws ​one die and squares the number that ​appears on ​it. Who ​has the better chance of getting the number ​36? Why?
   Show answer

   Peehu has the better chance. $P_{Peehu}=\frac{1}{6}$ while $P_{Apoorv}=\frac{1}{36}$.

   Step-by-step solution →
4. Q44 Exemplar · Exercise 13.2
   When we toss a ​coin, ​there are two ​possible ​outcomes - Head or Tail. Therefore, ​the probability of ​each outcome is $\frac{1}{2}$. Justify ​your answer.
   Show answer

   Yes, the statement is correct provided the coin is fair: Head and Tail are then equally likely, so each has probability $\frac{1}{2}$.

   Step-by-step solution →
5. Q45 Exemplar · Exercise 13.2
   A student says that if you throw a die, it will show up 1 or not ​1. ​Therefore, the probability of ​getting 1 and the probability of getting 'not ​1' each is equal to $\frac{1}{2}$. Is this correct? ​Give reasons.
   Show answer

   No, the student is incorrect. $P(1)=\frac{1}{6}$ and $P(\text{not }1)=\frac{5}{6}$; the two events are not equally likely.

   Step-by-step solution →
6. Q46 Exemplar · Exercise 13.2
   I toss ​three ​coins together. ​The possible ​outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say ​that probability of no ​heads is $\frac{1}{4}$. What ​is wrong with this conclusion?
   Show answer

   The four listed events are not equally likely, so dividing by 4 is wrong; the correct probability of no heads is $\frac{1}{8}$.

   Step-by-step solution →
7. Q47 Exemplar · Exercise 13.2
   If you toss a coin ​6 times and it comes ​down heads on each occasion, ​can ​you say that the ​probability ​of getting ​a head is 1? Give reasons.
   Show answer

   No. Getting 6 heads is just one chance outcome (probability $1/64$, not impossible). The probability of a head for a fair coin stays $1/2$; only a very large number of trials would make the experimental ratio approach $1/2$.

   Step-by-step solution →
8. Q48 Exemplar · Exercise 13.2
   Sushma ​tosses a ​coin 3 times and gets tail each time. Do you think that the ​outcome ​of next ​toss will ​be ​a tail? Give reasons.
   Show answer

   No. Each toss is independent, so the next toss is still equally likely to be a head or a tail, each with probability $\frac{1}{2}$.

   Step-by-step solution →
9. Q49 Exemplar · Exercise 13.2
   If I toss a ​coin 3 times ​and get head each ​time, should I expect a tail to have a ​higher chance in the ​4th toss? ​Give reason ​in ​support of your answer.
   Show answer

   No - the 4th toss is independent of the first three, so a tail still has probability $\frac{1}{2}$.

   Step-by-step solution →
10. Q50 Exemplar · Exercise 13.2
    A bag contains slips numbered from 1 to 100. ​If Fatima chooses a slip at ​random ​from the ​bag, it will either be an ​odd number or an even number. Since ​this situation has only two possible outcomes, ​so, the probability of each is $\frac{1}{2}$. Justify.
    Show answer

    Yes, each probability is $\frac{1}{2}$, but the justification 'two outcomes so 1/2 each' is wrong. It is 1/2 because there are exactly 50 odd and 50 even numbers among the 100 slips.

    Step-by-step solution →
11. Q51 CBSE 2026
    A letter is ​selected ​from ​the letters of the word ​FEBRUARY. The probability that it is a vowel is ​:

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

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

    Step-by-step solution →
12. Q52 CBSE 2026
    Two ​dice are rolled together. The probability ​that the ​sum of ​the ​numbers ​obtained is divisible ​by $6$, ​is :

    1. (a)$\frac{1}{6}$
    2. (b)$\frac{11}{36}$
    3. (c)$\frac{1}{12}$
    4. (d)$\frac{1}{4}$
    Show answer

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

    Step-by-step solution →
13. Q53 CBSE 2026
    Probability of ​getting ​an irrational ​number ​at random from ​the ​numbers $\sqrt{3},\sqrt{4},3\sqrt{9},3\sqrt{8},\sqrt{5},0,4^{\frac{3}{2}}$ ​is :

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

    (c) $\frac{3}{7}$

    Step-by-step solution →
14. Q54 CBSE 2026
    The probability ​of ​getting ​sum greater ​than $10$, ​when two dice are rolled ​together, ​is

    1. (a)$\frac{1}{9}$
    2. (b)$\frac{1}{18}$
    3. (c)$\frac{1}{12}$
    4. (d)$1$
    Show answer

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

    Step-by-step solution →
15. Q55 CBSE 2026
    A card is drawn from a well shuffled deck ​of $52$ cards. The ​probability of getting ​an ​ace ​or ​a ten is:

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

    (b) $\frac{2}{13}$

    Step-by-step solution →
16. Q56 CBSE 2026
    Two different ​dice are ​rolled together. ​The ​probability that ​both the ​obtained numbers ​are less ​than $4$, is

    1. (a)$\frac{2}{9}$
    2. (b)$\frac{7}{36}$
    3. (c)$\frac{1}{4}$
    4. (d)$\frac{2}{3}$
    Show answer

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

    Step-by-step solution →
17. Q57 CBSE 2026
    Which ​of the following ​can not be the probability of ​an ​event?

    1. (a)$\frac{39}{100}$
    2. (b)$\frac{0.001}{20}$
    3. (c)$\frac{10}{0.2}$
    4. (d)$10\%$
    Show answer

    (c) $\frac{10}{0.2}$

    Step-by-step solution →
18. Q58 CBSE 2026
    A card is ​drawn at random from a well shuffled ​deck of $52$ ​playing cards. The ​probability that it is either a ten or a ​king ​is :

    1. (a)$\frac{1}{26}$
    2. (b)$\frac{2}{13}$
    3. (c)$\frac{1}{13}$
    4. (d)$\frac{8}{26}$
    Show answer

    (b) $\frac{2}{13}$

    Step-by-step solution →
19. Q59 CBSE 2026
    A bag contains some red and some white balls. A ball is ​drawn at random ​from ​the ​bag. If the probability of getting a red ball is $\frac{2}{7}$, then the probability ​of getting ​a white ball ​is

    1. (a)$\frac{1}{14}$
    2. (b)$\frac{5}{7}$
    3. (c)$\frac{1}{7}$
    4. (d)$\frac{2}{7}$
    Show answer

    (b) $\frac{5}{7}$

    Step-by-step solution →
20. Q60 CBSE 2026
    One ​ticket is drawn at random ​from ​a bag containing $50$ tickets numbered $1$ to $50$. The probability ​that the drawn ticket has ​a number which is a multiple of $7$ is ​:

    1. (a)$\frac{1}{5}$
    2. (b)$\frac{7}{50}$
    3. (c)$\frac{3}{25}$
    4. (d)$\frac{4}{25}$
    Show answer

    (b) $\frac{7}{50}$

    Step-by-step solution →