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 12 of 20

1. Q221 CBSE 2024
   $Familystructure:$ In ​a recent survey of this year, 51% of the families ​had ​no children, ​20% ​had one child, 19% ​had two children, 7% had three children and 3% ​had four or more children. ​A family is selected at random.

   1. (i)Find the probability that the selected family has two or three children.[1]
   2. (ii)Find the probability that the selected family has more than one child.[1]
   3. (iii)(a)Find the probability that the selected family has less than three children.[2]
   4. (iii)(b)Find the probability that the selected family has more than two children. (OR)[2]
   Show answer

   (i) $P(\text{two or three})=\frac{26}{100}=\frac{13}{50}=0.26$; (ii) $P(\text{more than one})=\frac{29}{100}=0.29$; (iii)(a) $P(\text{less than three})=\frac{90}{100}=\frac{9}{10}=0.9$; (iii)(b) $P(\text{more than two})=\frac{10}{100}=\frac{1}{10}=0.1$

   Step-by-step solution →
2. Q222 CBSE 2024
   In ​a survey on holidays, $120$ people were asked to state ​which type of transport they used on ​their last ​holiday. The ​following pie chart shows the results ​of the survey. Observe the pie chart and answer the following ​questions.

   1. (i)If one person is selected at random, find the probability that he/she travelled by bus or ship.[1]
   2. (ii)Which is most favourite mode of transport and how many people used it ?[1]
   3. (iii)(a)A person is selected at random. If the probability that he did not use train is $4/5$, find the number of people who used train.[2]
   4. (iii)(b)(OR) The probability that randomly selected person used aeroplane is $7/60$. Find the revenue collected by air company at the rate of Rs. $5,000$ per person.[2]
   Show answer

   (i) The probability is $\frac{23}{120}$; (ii) Car is the most favourite mode, used by $59$ people; (iii)(a) $24$ people used the train; (iii)(b) The revenue is ₹70,000 (from $14$ aeroplane passengers).

   Step-by-step solution →
3. Q223 CBSE 2023
   In a family of two ​children, ​the ​probability ​of having at least ​one girl ​is ​:

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

   (c) $\frac{3}{4}$

   Step-by-step solution →
4. Q224 CBSE 2023
   A ​card ​is drawn ​at random from a well-shuffled deck of $52$ cards. ​The ​probability of getting ​a ​red card is:

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

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

   Step-by-step solution →
5. Q225 CBSE 2023
   One ​card is ​drawn ​at random from ​a well shuffled deck ​of 52 playing cards. ​What is ​the probability of getting '4 of hearts' ?

   1. (a)$\frac{1}{52}$
   2. (b)$\frac{1}{13}$
   3. (c)$\frac{1}{26}$
   4. (d)$\frac{1}{6}$
   Show answer

   (a) $\frac{1}{52}$

   Step-by-step solution →
6. Q226 CBSE 2023
   One card ​is drawn at ​random from a ​well-shuffled deck ​of $52$ playing ​cards. What is the ​probability of getting a black ​king?

   1. (a)$\frac{1}{26}$
   2. (b)$\frac{1}{13}$
   3. (c)$\frac{1}{52}$
   4. (d)$\frac{1}{2}$
   Show answer

   (a) $\frac{1}{26}$

   Step-by-step solution →
7. Q227 CBSE 2023
   Which of the ​following **cannot** be ​the probability of ​an ​event ​?

   1. (a)$0.1$
   2. (b)$\frac{5}{3}$
   3. (c)$3\%$
   4. (d)$\frac{1}{3}$
   Show answer

   (b) $\frac{5}{3}$

   Step-by-step solution →
8. Q228 CBSE 2023
   A bag contains $100$ cards numbered $1$ ​to $100$. A card is ​drawn ​at random from the bag. What is ​the probability that the number on ​the ​card is a ​perfect ​cube?

   1. (a)$\frac{1}{20}$
   2. (b)$\frac{3}{50}$
   3. (c)$\frac{1}{25}$
   4. (d)$\frac{7}{100}$
   Show answer

   (c) $\frac{1}{25}$

   Step-by-step solution →
9. Q229 CBSE 2023
   A die is ​rolled ​once. The probability that ​a composite ​number ​comes up, is ​:

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

   (c) $\frac{1}{3}$

   Step-by-step solution →
10. Q230 CBSE 2023
    If three ​coins ​are ​tossed simultaneously, ​what is the ​probability of getting ​at most one tail?

    1. (a)$\frac{3}{8}$
    2. (b)$\frac{4}{8}$
    3. (c)$\frac{5}{8}$
    4. (d)$\frac{7}{8}$
    Show answer

    (b) $\frac{4}{8}$

    Step-by-step solution →
11. Q231 CBSE 2023
    Two dice are ​thrown ​together. The probability ​of getting the difference ​of numbers ​on ​their upper faces equals to 3 ​is ​:

    1. (a)$\frac{1}{9}$
    2. (b)$\frac{2}{9}$
    3. (c)$\frac{1}{6}$
    4. (d)$\frac{1}{12}$
    Show answer

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

    Step-by-step solution →
12. Q232 CBSE 2023
    A die is thrown ​once. ​Find ​the ​probability of ​getting a number less than $7$.

    1. (a)$\frac{5}{6}$
    2. (b)$1$
    3. (c)$\frac{1}{6}$
    4. (d)$0$
    Show answer

    (b) $1$

    Step-by-step solution →
13. Q233 CBSE 2023
    A bag contains ​5 pink, ​8 blue ​and 7 yellow balls. One ​ball is ​drawn at ​random from the bag. What is the probability of ​getting neither a blue ​nor a pink ball?

    1. (a)$\frac{1}{4}$
    2. (b)$\frac{2}{5}$
    3. (c)$\frac{7}{20}$
    4. (d)$\frac{13}{20}$
    Show answer

    (c) $\frac{7}{20}$

    Step-by-step solution →
14. Q234 CBSE 2023
    A ​die ​is ​rolled ​once. The ​probability that the ​obtained number is more ​than $5$, ​is:

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

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

    Step-by-step solution →
15. Q235 CBSE 2023
    From a ​well-shuffled deck of $52$ playing cards, a card is drawn at ​random. ​What ​is ​the ​probability of getting ​a red ​queen ?

    1. (a)$\frac{1}{52}$
    2. (b)$\frac{1}{26}$
    3. (c)$\frac{1}{13}$
    4. (d)$\frac{12}{13}$
    Show answer

    (b) $\frac{1}{26}$

    Step-by-step solution →
16. Q236 CBSE 2023
    Which ​of the following ​numbers $cannot$ be ​the probability ​of an event ​?

    1. (a)$0.5$
    2. (b)$5\%$
    3. (c)$\frac{1}{0.5}$
    4. (d)$\frac{0.5}{14}$
    Show answer

    (c) $\frac{1}{0.5}$

    Step-by-step solution →
17. Q237 CBSE 2023
    Two ​coins are ​tossed together. ​The ​probability ​of getting at least one tail is ​:

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

    (c) $\frac{3}{4}$

    Step-by-step solution →
18. Q238 CBSE 2023
    A card is ​drawn at random from a ​well shuffled ​deck of ​52 ​playing cards. The probability of getting a ​face ​card is

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

    (b) $\frac{3}{13}$

    Step-by-step solution →
19. Q239 CBSE 2023
    A number is ​chosen at ​random from numbers 1 ​to ​20. The ​probability ​that it is a prime number, is ​:

    1. (a)$\frac{7}{20}$
    2. (b)$\frac{3}{10}$
    3. (c)$\frac{1}{2}$
    4. (d)$\frac{2}{5}$
    Show answer

    (d) $\frac{2}{5}$

    Step-by-step solution →
20. Q240 CBSE 2023
    Probability ​of happening of an event is denoted by $p$ and probability of ​non-happening of the event ​is denoted by $q$. Relation between $p$ ​and $q$ ​is

    1. (a)$p+q=1$
    2. (b)$p=1,q=1$
    3. (c)$p=q-1$
    4. (d)$p+q+1=0$
    Show answer

    (a) $p+q=1$

    Step-by-step solution →