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 15 of 20

1. Q281 CBSE 2020
   A ​number is selected at ​random from the numbers $1$ to $20$. ​The probability ​that the ​selected ​number is a ​multiple of $3$ is ____.
   Show answer

   $P(\text{multiple of }3)=\frac{3}{10}$

   Step-by-step solution →
2. Q282 CBSE 2020
   Two dice are thrown ​simultaneously. Find ​the probability ​that the ​sum of numbers appearing on the ​dice is ​six.
   Show answer

   $P(\text{sum}=6)=\frac{5}{36}$.

   Step-by-step solution →
3. Q283 CBSE 2020
   A letter ​of English ​alphabet is chosen ​at ​random. What ​is the ​probability that the ​chosen letter is a ​consonant?
   Show answer

   $P(\text{consonant})=\frac{21}{26}$.

   Step-by-step solution →
4. Q284 CBSE 2020
   If a pair of ​dice is thrown ​once, ​then what ​is ​the probability of getting a ​sum of $8$?
   Show answer

   $P(\text{sum}=8)=\frac{5}{36}$

   Step-by-step solution →
5. Q285 CBSE 2020
   A ​card is ​drawn at random ​from a ​well ​shuffled deck of $52$ playing cards. What is the probability ​of getting a black ​king ?
   Show answer

   $P(\text{black king})=\frac{1}{26}$

   Step-by-step solution →
6. Q286 CBSE 2020
   Two dice ​are ​thrown simultaneously. What is ​the probability that the sum of ​the two numbers ​appearing ​on the top is 13?
   Show answer

   $P(\text{sum}=13)=0$

   Step-by-step solution →
7. Q287 CBSE 2020
   If a ​number $x$ is ​chosen at random ​from the ​numbers $-3,-2,-1,0,1,2,3$, ​then ​find the probability of $x^2<4$.
   Show answer

   $P(x^2<4)=\frac{3}{7}$.

   Step-by-step solution →
8. Q288 CBSE 2020
   What ​is the probability ​that a randomly ​taken ​leap ​year has $52$ Sundays?
   Show answer

   The probability is $\frac{5}{7}$.

   Step-by-step solution →
9. Q289 CBSE 2020
   The ​probability that it will rain tomorrow ​is $0.85$. What ​is the probability that it will ​not rain ​tomorrow?
   Show answer

   $P(\text{not rain})=0.15$

   Step-by-step solution →
10. Q290 CBSE 2020
    A die is thrown ​once. What ​is the probability ​of getting a number ​less ​than ​3?
    Show answer

    $P(\text{number}<3)=\frac{2}{6}=\frac{1}{3}$

    Step-by-step solution →
11. Q291 CBSE 2020
    If the probability ​of winning a ​game ​is 0.07, ​what is the ​probability of losing it?
    Show answer

    $P(\text{losing})=0.93$

    Step-by-step solution →
12. Q292 CBSE 2020
    A ​die is thrown ​once. What ​is the ​probability of getting ​a ​prime number?
    Show answer

    $P(\text{prime})=\frac{1}{2}$.

    Step-by-step solution →
13. Q293 CBSE 2020
    A letter ​of English alphabet ​is chosen at random. ​Determine the probability ​that ​chosen ​letter ​is a consonant.
    Show answer

    $P(\text{consonant})=\frac{21}{26}$

    Step-by-step solution →
14. Q294 CBSE 2020
    A bag ​contains 5 red, ​8 white ​and 7 black balls. A ball is drawn at random from the bag. Find ​the probability that the drawn ball is

    1. (i)red or ​white
    2. (ii)not a ​white ball

    1. ired or white
    2. iinot a white ball
    Show answer

    $P(\text{red or white})=\frac{13}{20}$ and $P(\text{not white})=\frac{3}{5}$.

    Step-by-step solution →
15. Q295 CBSE 2020
    In a lottery, ​there are ​10 prizes ​and ​25 blanks. What is the ​probability of ​getting a ​prize?
    Show answer

    $P(\text{prize})=\frac{2}{7}$.

    Step-by-step solution →
16. Q296 CBSE 2020
    A bag contains $5$ red ​balls ​and some blue balls. If ​the probability of drawing a blue ball at random ​from the bag ​is three times that of a red ball, find ​the ​number of blue balls in the ​bag.
    Show answer

    The bag contains $15$ blue balls.

    Step-by-step solution →
17. Q297 CBSE 2020
    There ​are $16$ cards bearing numbers $1,2,3,\dots ,16$ ​in a bag. A card is drawn ​at ​random ​from the bag. Find the probability of getting a card having a multiple of $3$ ​on it.
    Show answer

    $P(\text{multiple of }3)=\frac{5}{16}$.

    Step-by-step solution →
18. Q298 CBSE 2020
    In ​a family of ​three children, ​find ​the probability of having at ​least two ​boys.
    Show answer

    $P(\text{at least two boys})=\frac{4}{8}=\frac{1}{2}$

    Step-by-step solution →
19. Q299 CBSE 2020
    Two dice ​are ​thrown ​at the same time. Find ​the ​probability ​of getting different numbers ​on the two dice.
    Show answer

    $P(\text{different numbers})=\frac{5}{6}$.

    Step-by-step solution →
20. Q300 CBSE 2020
    Two ​dice ​are thrown at ​the same time. Find ​the probability ​that the sum of the two ​numbers appearing on the ​top of the ​dice is more than $9$.
    Show answer

    $P(\text{sum}>9)=\frac{6}{36}=\frac{1}{6}$.

    Step-by-step solution →