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 1 of 5

1. Q1 NCERT · Exercise 14.1
   Complete the following statements:

   1. (i)Probability of an event E + Probability of the event 'not E' = ____.
   2. (ii)​The probability of an ​event that cannot ​happen is ____. Such an event is called ____.
   3. (iii)The probability of an event that is certain to happen is ____. Such an event is called ____.
   4. (iv)The sum ​of the probabilities of all the elementary events of an ​experiment is ____.
   5. (v)The probability of an event is greater ​than or equal to ____ and ​less than or equal ​to ____.
   Show answer

   (i) $1$; (ii) $0$, an impossible event; (iii) $1$, a sure (certain) event; (iv) $1$; (v) $0$ and $1$.

   Step-by-step solution →
2. Q2 NCERT · Exercise 14.1
   Which of the following ​experiments ​have equally likely outcomes? ​Explain.

   1. (i)A driver attempts to start a car. ​The car starts ​or does not start.
   2. (ii)A player attempts to shoot a basketball. She/he shoots or misses the shot.
   3. (iii)A trial is made to answer a true-false question. The answer is right or ​wrong.
   4. (iv)A baby is born. ​It is a boy or a girl.
   Show answer

   (i) Not equally likely — the car starting depends on its condition. (ii) Not equally likely — shooting depends on the player's skill. (iii) Equally likely — a random guess favours neither answer. (iv) Equally likely — a boy and a girl have no built-in bias.

   Step-by-step solution →
3. Q3 NCERT · Exercise 14.1
   Why ​is tossing ​a coin considered ​to ​be ​a fair way of deciding which team ​should get the ball at the beginning of a ​football game?
   Show answer

   Tossing an unbiased coin gives two equally-likely outcomes, so $P(\text{head})=P(\text{tail})=\frac{1}{2}$. Each team is tied to one outcome, hence each has an equal $\frac{1}{2}$ chance and no team is favoured — that is why the toss is fair.

   Step-by-step solution →
4. Q4 NCERT · Exercise 14.1
   Which ​of the ​following cannot ​be ​the ​probability of ​an event?

   1. (a)$\frac{2}{3}$
   2. (b)$-1.5$
   3. (c)$15\%$
   4. (d)$0.7$
   Show answer

   (b) $-1.5$

   Step-by-step solution →
5. Q5 NCERT · Exercise 14.1
   If $P(E)=0.05$, what is ​the ​probability ​of ​'not ​E'?
   Show answer

   $P(\text{not }E)=0.95$.

   Step-by-step solution →
6. Q6 NCERT · Exercise 14.1
   A bag contains ​lemon flavoured ​candies ​only. ​Malini takes out one candy without looking into the bag. What is the ​probability that she takes out ​

   1. (i)an orange flavoured candy?
   2. (ii)a lemon flavoured candy?
   Show answer

   (i) $P(\text{orange})=0$ (impossible event); (ii) $P(\text{lemon})=1$ (sure event).

   Step-by-step solution →
7. Q7 NCERT · Exercise 14.1
   It is given that ​in a group ​of 3 students, the probability ​of 2 students not having the same birthday is $0.992$. What is ​the probability ​that the ​2 ​students have the same birthday?
   Show answer

   $P(\text{same birthday})=1-0.992=0.008$.

   Step-by-step solution →
8. Q8 NCERT · Exercise 14.1
   A bag contains $3$ red balls ​and $5$ black ​balls. A ball is drawn at random from ​the bag. What ​is the probability that the ​ball drawn is

   1. (i)​red?
   2. (ii)not red?
   Show answer

   (i) $P(\text{red})=\frac{3}{8}$; (ii) $P(\text{not red})=\frac{5}{8}$.

   Step-by-step solution →
9. Q9 NCERT · Exercise 14.1
   A box contains $5$ red ​marbles, $8$ white ​marbles ​and $4$ green ​marbles. One marble is taken out of the box at random. What is the ​probability that the marble taken out ​will be ​

   1. (i)red?
   2. (ii)white?
   3. (iii)not ​green?
   Show answer

   (i) $P(\text{red})=\frac{5}{17}$; (ii) $P(\text{white})=\frac{8}{17}$; (iii) $P(\text{not green})=\frac{13}{17}$.

   Step-by-step solution →
10. Q10 NCERT · Exercise 14.1
    A piggy bank contains hundred 50p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 ​coins. If it is equally likely ​that one of the coins will fall out when ​the ​bank is turned upside down, what is the probability that ​the ​coin

    1. (i)will be a 50 p coin?
    2. (ii)will ​not be ​a Rs 5 coin?
    Show answer

    (i) $P(50\text{p})=\frac{5}{9}$; (ii) $P(\text{not Rs}5)=\frac{17}{18}$.

    Step-by-step solution →
11. Q11 NCERT · Exercise 14.1
    Gopi buys a fish from a ​shop for his ​aquarium. The shopkeeper takes ​out one fish at random from a tank containing $5$ male fish and $8$ female fish (see Fig. 14.4). ​What is ​the probability that the fish taken out is a ​male ​fish?

    Show answer

    $P(\text{male fish})=\frac{5}{13}$.

    Step-by-step solution →
12. Q12 NCERT · Exercise 14.1
    A game of chance consists of spinning an arrow ​which ​comes to rest pointing at one of the numbers $1,2,3,4,5,6,7,8$ (see Fig. ​14.5), and ​these are equally likely outcomes. What is the probability that it will point ​at

    1. (i)$8$? ​
    2. (ii)an ​odd number?
    3. (iii)a number greater than $2$?
    4. (iv)a number less than $9$?

    Show answer

    (i) $\frac{1}{8}$; (ii) $\frac{1}{2}$; (iii) $\frac{3}{4}$; (iv) $1$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 14.1
    A die is thrown ​once. Find the ​probability of getting

    1. (i)a prime ​number;
    2. (ii)​a number ​lying between 2 ​and 6;
    3. (iii)an odd number.
    Show answer

    (i) $P(\text{prime})=\frac{1}{2}$; (ii) $P(\text{between }2\text{ and }6)=\frac{1}{2}$; (iii) $P(\text{odd})=\frac{1}{2}$.

    Step-by-step solution →
14. Q14 NCERT · Exercise 14.1
    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)a face card
    3. (iii)a red ​face ​card
    4. (iv)​the jack of hearts
    5. (v)a spade ​
    6. (vi)the queen of diamonds
    Show answer

    (i) $\frac{1}{26}$; (ii) $\frac{3}{13}$; (iii) $\frac{3}{26}$; (iv) $\frac{1}{52}$; (v) $\frac{1}{4}$; (vi) $\frac{1}{52}$.

    Step-by-step solution →
15. Q15 NCERT · Exercise 14.1
    Five cards - the ten, jack, ​queen, king and ​ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

    1. (i)What ​is the probability ​that the card is the queen? ​
    2. (ii)​If the queen is ​drawn and put aside, what is the probability that the second card ​picked up is (a) an ace? (b) a queen?
    Show answer

    (i) $P(\text{queen})=\frac{1}{5}$; (ii)(a) $P(\text{ace})=\frac{1}{4}$; (ii)(b) $P(\text{queen})=0$.

    Step-by-step solution →
16. Q16 NCERT · Exercise 14.1
    12 defective pens are accidentally mixed with 132 good ones. It ​is not ​possible to just ​look at a pen and tell ​whether or not it is defective. One ​pen is ​taken out at random ​from this lot. Determine the probability that the pen taken ​out is a good one.
    Show answer

    $P(\text{good pen})=\frac{11}{12}$.

    Step-by-step solution →
17. Q17 NCERT · Exercise 14.1
    1. (i)A lot ​of 20 ​bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this ​bulb is defective?
    2. (ii)Suppose the bulb ​drawn in (i) is not defective and ​is not ​replaced. Now one bulb is drawn at random from the rest. What is ​the probability that this bulb is not defective?
    Show answer

    (i) $P(\text{defective})=\frac{1}{5}$; (ii) $P(\text{not defective})=\frac{15}{19}$.

    Step-by-step solution →
18. Q18 NCERT · Exercise 14.1
    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 number ​divisible by $5$.
    Show answer

    (i) $P(\text{two-digit})=\frac{9}{10}$; (ii) $P(\text{perfect square})=\frac{1}{10}$; (iii) $P(\text{divisible by }5)=\frac{1}{5}$.

    Step-by-step solution →
19. Q19 NCERT · Exercise 14.1
    A child has a ​die whose six ​faces show the letters ​A, ​B, C, D, ​E, ​A. The die is thrown once. ​What is the probability of getting ​

    1. (i)$A$?
    2. (ii)$D$?
    Show answer

    (i) $P(A)=\frac{1}{3}$; (ii) $P(D)=\frac{1}{6}$.

    Step-by-step solution →
20. Q20 NCERT · Exercise 14.1
    Suppose you drop ​a die ​at random on ​the ​rectangular region ​shown in Fig. 14.6. ​What is the probability ​that ​it will land inside the circle with diameter $1\text{m}$?

    Show answer

    $P(\text{lands inside the circle})=\frac{\pi }{24}\approx 0.131$.

    Step-by-step solution →