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 19 of 20

1. Q361 CBSE 2016
   Two ​dice of different colours are thrown at ​the same time. Write down all ​the possible outcomes. Find the probability that ​the sum of two numbers appearing on the top of ​dice is a ​multiple of $5$.
   Show answer

   The probability that the sum is a multiple of 5 is $\frac{7}{36}$.

   Step-by-step solution →
2. Q362 CBSE 2016
   A game consist ​of tossing a ​one-rupee coin 3 times and noting ​the ​outcome each ​time. Ramesh will win the game if all the tosses show the same result, (i.e. either all three heads or all three tails) and loses the ​game otherwise. Find the probability that Ramesh will lose ​the game.
   Show answer

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

   Step-by-step solution →
3. Q363 CBSE 2016
   Three ​different coins are ​tossed together. Find the ​probability ​of ​getting

   1. (i)​exactly two heads
   2. (ii)at least two heads
   3. (iii)at ​least two tails.

   1. iexactly two heads
   2. iiat least two heads
   3. iiiat least two tails
   Show answer

   $P(\text{exactly two heads})=\frac{3}{8}$, $P(\text{at least two heads})=\frac{1}{2}$, $P(\text{at least two tails})=\frac{1}{2}$.

   Step-by-step solution →
4. Q364 CBSE 2016
   A number $x$ is selected at random from ​the numbers $1,2,3$ and $4$. Another number $y$ ​is ​selected at random from the ​numbers $1,4,9$ and $16$. ​Find the probability ​that product of $x$ and $y$ ​is ​less than $16$.
   Show answer

   $P(xy<16)=\frac{8}{16}=\frac{1}{2}$.

   Step-by-step solution →
5. Q365 CBSE 2016
   A ​die is thrown twice. Find the probability ​that ​:

   1. (i)$5$ will not ​come either time.
   2. (ii)​Sum of numbers on the two dice is ​not more ​than $5$.

   1. (i)$5$ will not come either time.
   2. (ii)Sum of numbers on the two dice is not more than $5$.
   Show answer

   (i) $P=\frac{25}{36}$. (ii) $P=\frac{10}{36}=\frac{5}{18}$.

   Step-by-step solution →
6. Q366 CBSE 2016
   A ​game of chance consists of spinning ​an arrow on a circular board, divided into $8$ equal parts, which ​comes to rest pointing at one of the numbers $1,2,3,\dots ,8$ ​(Fig. 9), which are equally likely ​outcomes. What is the probability that the ​arrow will point at

   1. (i)​an odd number
   2. (ii)a number greater than $3$
   3. (iii)a number less than $9$.

   1. iProbability the arrow points at an odd number.
   2. iiProbability the arrow points at a number greater than $3$.
   3. iiiProbability the arrow points at a number less than $9$.
   Show answer

   (i) $P(\text{odd})=\frac{1}{2}$; (ii) $P(>3)=\frac{5}{8}$; (iii) $P(<9)=1$.

   Step-by-step solution →
7. Q367 CBSE 2016
   In ​Fig. ​7 is shown a disc on which a player spins an arrow twice. The fraction $\frac{a}{b}$ is formed, where 'a' is the number of sector ​on which arrow stops on the first spin and 'b' is the number of the sector in ​which ​the arrow stops on second spin. On ​each spin, each ​sector has equal chance of selection by the arrow. Find the probability that the fraction $\frac{a}{b}>1$.

   Show answer

   $P\left(\frac{a}{b}>1\right)=\frac{15}{36}=\frac{5}{12}$.

   Step-by-step solution →
8. Q368 CBSE 2016
   The King, Queen and Jack of clubs are removed from a deck ​of $52$ playing cards and the remaining cards are then well shuffled. Now a card is drawn ​at random from the remaining cards. Determine the ​probability ​that the drawn card is:

   1. (i)a card of hearts
   2. (ii)a red jack
   3. (iii)​a black ​card.

   1. ia card of hearts
   2. iia red jack
   3. iiia black card
   Show answer

   (i) $P(\text{heart})=\frac{13}{49}$; (ii) $P(\text{red jack})=\frac{2}{49}$; (iii) $P(\text{black card})=\frac{23}{49}$.

   Step-by-step solution →
9. Q369 CBSE 2016
   A number $x$ is selected ​at random from the ​numbers $1,2,3$ and $4$. ​Another number $y$ is selected at random ​from the numbers $1,4,9$ ​and $16$. Find the probability that the ​product of $x$ and $y$ ​is ​less than $16$.
   Show answer

   $P(xy<16)=\frac{8}{16}=\frac{1}{2}$.

   Step-by-step solution →
10. Q370 CBSE 2016
    A number $x$ is ​selected at random from the ​numbers $1,4,9,16$ and another number $y$ is ​selected at random from ​the numbers $1,2,3,4$. ​Find the ​probability that the value of $xy$ is more than $16$.
    Show answer

    $P(xy>16)=\frac{6}{16}=\frac{3}{8}$.

    Step-by-step solution →
11. Q371 CBSE 2015
    A game ​of ​chance consists of spinning an ​arrow ​which comes to rest pointing at one of the ​numbers $1,2,3,4,5,6,7,8$ and these are equally likely outcomes. ​Find ​the probability that the arrow will point at ​any factor of $8$.
    Show answer

    $P(\text{factor of }8)=\frac{1}{2}$

    Step-by-step solution →
12. Q372 CBSE 2015
    Two different dice are tossed ​together. ​Find the ​probability that ​the ​product of the ​two ​numbers on the top of the ​dice is 6.
    Show answer

    $P(\text{product}=6)=\frac{4}{36}=\frac{1}{9}$

    Step-by-step solution →
13. Q373 CBSE 2015
    A letter of ​English ​alphabet ​is chosen at ​random. Determine ​the probability that ​the chosen letter is a ​consonant.
    Show answer

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

    Step-by-step solution →
14. Q374 CBSE 2015
    From a deck ​of playing cards all ​aces ​and ​all hearts are removed. A card is then drawn from the ​remaining cards. Find the probability that ​it is a red face card.
    Show answer

    The probability is $\frac{3}{36}=\frac{1}{12}$.

    Step-by-step solution →
15. Q375 CBSE 2015
    A ​box ​contains cards ​numbered from $1$ to $15$. A card is drawn at random from the box. Find the probability that ​the drawn card bears ​a ​prime number.
    Show answer

    The probability is $\frac{6}{15}=\frac{2}{5}$.

    Step-by-step solution →
16. Q376 CBSE 2015
    A ​bag contains $18$ balls out of ​which $x$ balls are red.

    1. (i)If ​one ball is drawn ​at ​random from the bag, what is the probability that it is not red?
    2. (ii)If $2$ more red balls are ​put in ​the bag, the probability of drawing a red ball will be $\frac{9}{8}$ times the ​probability of drawing a red ball in the first case. Find the value of $x$.

    1. (i)If one ball is drawn at random from the bag, what is the probability that it is not red?
    2. (ii)If 2 more red balls are put in the bag, the probability of drawing a red ball will be $\frac{9}{8}$ times the probability of drawing a red ball in the first case. Find the value of $x$.
    Show answer

    (i) $P(\text{not red})=\frac{18-x}{18}$, which equals $\frac{10}{18}=\frac{5}{9}$ for $x=8$; (ii) $x=8$.

    Step-by-step solution →
17. Q377 CBSE 2015
    Two different ​dice are ​rolled ​together. Find the probability of getting :

    1. (i)the sum ​of ​numbers on ​two ​dice to be $5$.
    2. (ii)even numbers on both dice.

    1. (i)the sum of numbers on two dice to be $5$.
    2. (ii)even numbers on both dice.
    Show answer

    $P(\text{sum}=5)=\frac{1}{9}$ and $P(\text{both even})=\frac{1}{4}$.

    Step-by-step solution →
18. Q378 CBSE 2015
    The probability of ​selecting ​a red ball at random from ​a jar that contains only red, ​blue and orange balls is $\frac{1}{4}$. The probability of selecting a blue ball at random from the same jar is $\frac{1}{3}$. If the jar contains ​10 orange balls, find the total number of balls ​in the jar.
    Show answer

    The jar contains a total of $24$ balls.

    Step-by-step solution →
19. Q379 CBSE 2015
    A card is drawn at random ​from a ​well-shuffled deck of playing cards. ​Find ​the probability that the card ​drawn is

    1. (i)a ​card of spade or an ​ace.
    2. (ii)a black king.
    3. (iii)neither a jack nor a king.
    4. (iv)either a king or a queen.
    Show answer

    $(i)\frac{4}{13},(ii)\frac{1}{26},(iii)\frac{11}{13},(iv)\frac{2}{13}$.

    Step-by-step solution →
20. Q380 CBSE 2015
    A box contains cards ​bearing numbers from 6 to 70. If one card is drawn ​at random ​from the box, ​find the probability that it bears

    1. (i)a one digit number.
    2. (ii)a number divisible by 5.
    3. (iii)an odd number ​less than 30.
    4. (iv)a composite number between ​50 and 70.

    1. ia one digit number.
    2. iia number divisible by 5.
    3. iiian odd number less than 30.
    4. iva composite number between 50 and 70.
    Show answer

    (i) $\frac{4}{65}$, (ii) $\frac{1}{5}$, (iii) $\frac{12}{65}$, (iv) $\frac{3}{13}$.

    Step-by-step solution →