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 16 of 20

1. Q301 CBSE 2020
   Two different ​dice are ​thrown together, ​find the probability that ​the sum of the ​numbers appeared is less ​than ​5.
   Show answer

   $P(\text{sum}<5)=\frac{6}{36}=\frac{1}{6}$.

   Step-by-step solution →
2. Q302 CBSE 2020
   Find the probability that $5$ ​Sundays occur ​in the month ​of November ​of a ​randomly ​selected year.
   Show answer

   $P(5\text{ Sundays in November})=\frac{2}{7}$

   Step-by-step solution →
3. Q303 CBSE 2020
   A ​card is ​drawn at ​random from a pack ​of $52$ cards. Find ​the probability that the drawn ​card is ​a red ​face card.
   Show answer

   $P(\text{red face card})=\frac{6}{52}=\frac{3}{26}$.

   Step-by-step solution →
4. Q304 CBSE 2020
   All kings, ​queens and aces are ​removed from a pack of 52 playing ​cards and the remaining ​cards ​are well shuffled. A card is then drawn from the pack at random. What is the probability ​that

   1. (i)it is a face card, and
   2. (ii)a card of red colour?
   Show answer

   $P(\text{face card})=\frac{1}{10}$ and $P(\text{red card})=\frac{1}{2}$.

   Step-by-step solution →
5. Q305 CBSE 2020
   If ​a ​number $x$ ​is ​chosen at random from the ​numbers $-3,-2,-1,0,1,2,3$. What ​is ​the probability that $x^2\le 4$?
   Show answer

   $P(x^2\le 4)=\frac{5}{7}$

   Step-by-step solution →
6. Q306 CBSE 2020
   Find ​the probability that a ​leap ​year ​selected at random will ​contain $53$ ​Sundays ​and $53$ Mondays.
   Show answer

   $P=\frac{1}{7}$.

   Step-by-step solution →
7. Q307 CBSE 2020
   A ​child has a die whose ​six faces show the letters as shown ​below. The die is ​thrown ​once. What is the probability ​of getting ​

   1. (i)$A$,
   2. (ii)$D$?

   Letters on the six faces of the die

   Face 1	Face 2	Face 3	Face 4	Face 5	Face 6
   A	B	C	D	E	A

   Show answer

   $P(A)=\frac{1}{3}$ and $P(D)=\frac{1}{6}$.

   Step-by-step solution →
8. Q308 CBSE 2020
   A Group Housing ​Society ​has 600 members, ​who have their houses in the campus and decided to hold a Tree Plantation Drive on the occasion of New Year. Each household was given the choice of planting a ​sampling of its ​choice. ​The number of different types of saplings planted were as shown. On the opening ceremony, one of the plants is selected ​randomly for a prize. After reading the above passage, answer the following questions. What is the probability that the selected plant is

   Number of different types of saplings planted (total 600)

   Type of sapling	Number planted
   Neem	125
   Peepal	165
   Creepers	50
   Fruit plants	150
   Flowering plants	110

   1. iA fruit plant or a flowering plant ?[1]
   2. iiEither a Neem plant or a Peepal plant ?[1]
   Show answer

   (i) $P=\frac{13}{30}$; (ii) $P=\frac{29}{60}$

   Step-by-step solution →
9. Q309 CBSE 2020
   Two dice ​are ​tossed simultaneously. Find the probability of ​getting

   1. (i)an ​even number on ​both dice.
   2. (ii)the ​sum of two numbers more than 9.
   Show answer

   (i) $P(\text{even on both})=\frac{1}{4}$. (ii) $P(\text{sum}>9)=\frac{1}{6}$.

   Step-by-step solution →
10. Q310 CBSE 2020
    Two friends A and B take their breakfast occasionally ​in a restaurant which prepares a speciality dish on Monday, Wednesday and Sunday. Each is equally likely to visit the restaurant on any day on ​which the speciality dish is made. Find the ​probability ​that both will enjoy taking the speciality ​dish on the ​

    1. (i)​same day, and
    2. (ii)​different days.
    Show answer

    (i) $P(\text{same day})=\frac{1}{3}$; (ii) $P(\text{different days})=\frac{2}{3}$

    Step-by-step solution →
11. Q311 CBSE 2020
    Two coins are tossed ​together. Find ​the probability ​of getting

    1. (i)​both heads, and ​
    2. (ii)exactly one ​head.

    1. iboth heads
    2. iiexactly one head
    Show answer

    (i) $P(\text{both heads})=\frac{1}{4}$; (ii) $P(\text{exactly one head})=\frac{1}{2}$.

    Step-by-step solution →
12. Q312 CBSE 2020
    One card is drawn from a well-shuffled deck of ​52 cards. Find ​the ​probability of ​getting

    1. (i)a king ​of red colour.
    2. (ii)the queen of diamonds.
    3. (iii)an ace.

    1. (i)a king of red colour.
    2. (ii)the queen of diamonds.
    3. (iii)an ace.
    Show answer

    (i) $P=\frac{1}{26}$; (ii) $P=\frac{1}{52}$; (iii) $P=\frac{1}{13}$.

    Step-by-step solution →
13. Q313 CBSE 2020
    A ​box ​contains ​90 discs which ​are ​numbered from 1 to 90. If ​one ​disc is ​drawn at random from the box, find the probability that it bears

    1. (i)a two-digit number.
    2. (ii)a perfect square number.
    3. (iii)a prime number less than 15.
    Show answer

    (i) $\frac{9}{10}$, (ii) $\frac{1}{10}$, (iii) $\frac{1}{15}$.

    Step-by-step solution →
14. Q314 CBSE 2020
    Read the following passage and ​answer the questions given at ​the end : Diwali Fair A game in a booth at a Diwali ​Fair involves using a spinner first. ​Then, if ​the spinner ​stops on an even number, the player is allowed to pick a marble from a bag. ​The spinner and the marbles in the bag are represented in Figure-8. Prizes are given, when a black marble is ​picked. Shweta plays the game once.

    1. iWhat is the probability that she will be allowed to pick a marble from the bag?[1]
    2. iiSuppose she is allowed to pick a marble from the bag, what is the probability of getting a prize, when it is given that the bag contains $20$ balls out of which $6$ are black?[2]
    Show answer

    (i) $P(\text{allowed to pick})=\frac{5}{6}$; (ii) $P(\text{prize})=\frac{3}{10}$.

    Step-by-step solution →
15. Q315 CBSE 2019
    Two different ​dice are rolled. ​Find ​the probability ​of getting such ​numbers ​on the two dice whose product is ​a perfect square.
    Show answer

    $P(\text{product is a perfect square})=\frac{8}{36}=\frac{2}{9}$.

    Step-by-step solution →
16. Q316 CBSE 2019
    A bag ​contains $15$ ​balls, out of which some are white ​and ​the others are ​black. If the probability of drawing a ​black ball at random from the bag ​is $\frac{2}{3}$, then find how many white balls are ​there in the bag.
    Show answer

    There are $5$ white balls in the bag.

    Step-by-step solution →
17. Q317 CBSE 2019
    A ​card is ​drawn at random from a pack of $52$ playing ​cards. Find the probability of drawing ​a ​card which is neither a ​spade nor a king.
    Show answer

    $P(\text{neither a spade nor a king})=\frac{36}{52}=\frac{9}{13}$.

    Step-by-step solution →
18. Q318 CBSE 2019
    The probability of ​selecting a blue marble ​at random from a jar that contains only blue, black and green ​marbles is $\frac{1}{5}$. The probability ​of selecting a black marble at random from the ​same jar is $\frac{1}{4}$. If the jar contains $11$ green marbles, find ​the total number of ​marbles in ​the jar.
    Show answer

    Total number of marbles $=20$.

    Step-by-step solution →
19. Q319 CBSE 2019
    A child has a die whose $6$ faces show ​the letters given below: A, B, C, ​A, A, ​B. ​The die ​is thrown once. What ​is the probability ​of getting

    1. (i)A
    2. (ii)B?
    Show answer

    $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{3}$.

    Step-by-step solution →
20. Q320 CBSE 2019
    A game ​consists of tossing a ​coin $3$ ​times and noting the ​outcome each time. If getting the same result in ​all the tosses is a ​success, find the probability of losing the game.
    Show answer

    The probability of losing the game is $\frac{3}{4}$.

    Step-by-step solution →