CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Exemplar Solutions Class 10 Maths Chapter 13 Probability
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Boards begin February 2027
Pre-boards are in December
Probability is in Statistics and Probability, which carries 11 of the 80 marks in the 2026-27 CBSE Maths paper
17 NCERT Exemplar questions from Chapter 13
Exercise 13.1
Exemplar Ex 13.1 Q121 mark
If an event cannot occur, then its probability is
Step 1An event that cannot occur is called an impossible event.
Step-by-step solution
An event that cannot occur is called an impossible event.
Number of favourable outcomes for an impossible event is 0.
One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
Step 1Multiples of 5 in 1–40: 5, 10, 15, …, 40 → 8 numbers.
Step-by-step solution
Multiples of 5 in 1–40: 5, 10, 15, …, 40 → 8 numbers.
A bag contains 10 red, 5 blue and 7 green balls. A ball is drawn at random. Find the probability that the ball is (i) a red ball, (ii) not a blue ball.
The king, queen and jack of clubs are removed from a deck of 52 playing cards and then it is well-shuffled. One card is drawn at random. Find the probability that the card is (i) a heart, (ii) a king.
Step 1After removing K, Q, J of clubs, the deck has 52 − 3 = 49 cards.
Step-by-step solution
After removing K, Q, J of clubs, the deck has 52 − 3 = 49 cards.
(i) Hearts: still 13 cards. P(heart) = 13/49.
(ii) Kings remaining: 3 (the king of clubs was removed). P(king) = 3/49.
Cards numbered 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has (i) an even number, (ii) a square number.
Step 1Total cards = 101 − 2 + 1 = 100.
Step-by-step solution
Total cards = 101 − 2 + 1 = 100.
(i) Even numbers in 2–101: 2, 4, 6, …, 100 → count = 50. P = 50/100 = 1/2.
(ii) Square numbers in 2–101: 4, 9, 16, 25, 36, 49, 64, 81, 100 → 9 numbers. P = 9/100.
In a game the entry fee is ₹5. The game consists of tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back; if she throws 3 heads she gets double the entry fee; otherwise she loses. For tossing a coin three times, find the probability that she (i) loses the entry fee, (ii) gets double the entry fee, (iii) just gets her entry fee back.
Step 1[1 mark] The coin is tossed 3 times, so the sample space has 2³ = 8 equally likely outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Step-by-step solution
[1 mark] The coin is tossed 3 times, so the sample space has 2³ = 8 equally likely outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
[1 mark] (i) She loses only when no head shows (0 heads) — outcome TTT, i.e. 1 favourable outcome.
[1 mark] (i) P(loses the entry fee) = 1/8.
[1 mark] (ii) She gets double the fee only on 3 heads (HHH) — 1 outcome, so P(gets double) = 1/8.
[1 mark] (iii) She gets her fee back on exactly 1 or 2 heads = 8 − 1(HHH) − 1(TTT) = 6 outcomes, so P = 6/8 = 3/4.
A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. Find the value of x and then (i) the probability that the ball is not red, (ii) the probability that the ball is white.
Step 1[1 mark] Total number of balls = x + 2x + 3x = 6x, and this equals 24.
Step-by-step solution
[1 mark] Total number of balls = x + 2x + 3x = 6x, and this equals 24.
[1 mark] Solving 6x = 24 gives x = 4.
[1 mark] So red = x = 4, white = 2x = 8 and blue = 3x = 12.
[1 mark] (i) Number of non-red balls = 24 − 4 = 20, so P(not red) = 20/24 = 5/6.
[1 mark] (ii) Number of white balls = 8, so P(white) = 8/24 = 1/3.
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Questions from the NCERT Class 10 Mathematics Exemplar Problems; the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.