NCERT Solutions for Class 10 Maths Chapter 14 Probability (2026-27)

Class 10 Maths Chapter 14, Probability, has a single exercise (Exercise 14.1, 25 questions) in the current 2023-rationalised, 2026-27 session syllabus — the older optional Exercise 14.2 was removed in the rationalisation. Below are original, independently-derived solutions to all 25 questions. These Class 10 Mathematics Chapter 14 solutions are also useful as quick revision notes before exams.

Why This Chapter Matters for Boards

Probability is a short, high-scoring chapter that is almost entirely formula- and logic-based, using classic setups (coins, dice, cards, marbles) that repeat across CBSE board papers. Getting the total-outcomes count right (especially for two dice = 36, or a 52-card deck) is the single most common source of error.

Exercise 14.1 Solutions

1. Q1. Complete: (i) P(E)+P(not E)=___ (ii) P(impossible event)=___, called ___ (iii) P(sure event)=___, called ___ (iv) Sum of all elementary probabilities=___ (v) 0≤P(E)≤___
   Solution: (i) 1 (ii) 0, impossible event (iii) 1, sure/certain event (iv) 1 (v) 0 and 1.
2. Q2. Which of these have equally likely outcomes: (i) car starts/doesn’t (ii) basketball shot scores/misses (iii) true-false guess right/wrong (iv) baby born boy/girl?
   Solution: (i) and (ii) are skill/condition-dependent, not equally likely. (iii) and (iv) are treated as equally likely at this level.
3. Q3. Why is a coin toss a fair way to decide which team starts a football match?
   Solution: A coin has exactly 2 equally likely outcomes (head/tail), so neither team is favoured — each has probability 1/2.
4. Q4. Which cannot be a probability: (A) 2/3 (B) -1.5 (C) 15% (D) 0.7?
   Solution: Probability must satisfy 0≤P(E)≤1. Answer: (B) -1.5 (negative, invalid).
5. Q5. If P(E)=0.05, find P(not E).
   Solution: P(not E)=1-0.05=0.95.
6. Q6. A bag has only lemon-flavoured candies. Find P(orange) and P(lemon) on a random draw.
   Solution: P(orange)=0 (impossible); P(lemon)=1 (certain).
7. Q7. P(2 students don’t share a birthday)=0.992. Find P(they do share).
   Solution: P(share)=1-0.992=0.008.
8. Q8. A bag has 3 red, 5 black balls. Find P(red) and P(not red).
   Solution: Total=8. P(red)=3/8. P(not red)=1-3/8=5/8.
9. Q9. A box has 5 red, 8 white, 4 green marbles. Find P(red), P(white), P(not green).
   Solution: Total=17. P(red)=5/17. P(white)=8/17. P(green)=4/17 ⇒ P(not green)=13/17.
10. Q10. Piggy bank: 100 fifty-paisa, 50 one-rupee, 20 two-rupee, 10 five-rupee coins. Find P(50p) and P(not Rs5).
    Solution: Total=180. P(50p)=100/180=5/9. P(Rs5)=10/180 ⇒ P(not Rs5)=17/18.
11. Q11. Fish tank has 5 male, 8 female fish. Find P(male).
    Solution: Total=13. P(male)=5/13.
12. Q12. A spinner points to 1-8 equally likely. Find P(8), P(odd), P(>2), P(<9).
    Solution: Total=8. P(8)=1/8. P(odd)={1,3,5,7}=4/8=1/2. P(>2)=6/8=3/4. P(<9)=8/8=1 (sure).
13. Q13. A die is thrown once. Find P(prime), P(strictly between 2 and 6), P(odd).
    Solution: Total=6. Primes{2,3,5}=1/2. Between 2,6={3,4,5}=1/2. Odd{1,3,5}=1/2.
14. Q14. A card from 52. Find P(red king), P(face card), P(red face card), P(jack of hearts), P(spade), P(queen of diamonds).
    Solution: P(red king)=2/52=1/26. P(face)=12/52=3/13. P(red face)=6/52=3/26. P(jack of hearts)=1/52. P(spade)=13/52=1/4. P(queen of diamonds)=1/52.
15. Q15. 5 diamond cards (10,J,Q,K,A) shuffled face down. (i) P(queen)? (ii) Queen removed; from remaining find P(ace), P(queen).
    Solution: (i) 1/5. (ii) 4 left: P(ace)=1/4; P(queen)=0 (already removed).
16. Q16. 12 defective pens mixed with 132 good ones. Find P(good).
    Solution: Total=144. P(good)=132/144=11/12.
17. Q17. (i) 20 bulbs, 4 defective; find P(defective). (ii) One good bulb removed (not replaced); find P(non-defective) from rest.
    Solution: (i) 4/20=1/5. (ii) 19 left, 4 defective, 15 good ⇒ 15/19.
18. Q18. 90 discs numbered 1-90. Find P(two-digit), P(perfect square), P(divisible by 5).
    Solution: Two-digit(10-90)=81 ⇒ 9/10. Perfect squares{1,4,9,16,25,36,49,64,81}=9 ⇒ 1/10. Multiples of 5=18 ⇒ 1/5.
19. Q19. A die has faces A,B,C,D,E,A. Find P(A), P(D).
    Solution: P(A)=2/6=1/3. P(D)=1/6.
20. Q20. A tile dropped on a 3m×2m region with a 1m-diameter circle inside. Find P(lands in circle).
    Solution: Rectangle area=6 m². Circle area=π(0.5)²=π/4. P=(π/4)/6=π/24.
21. Q21. 144 pens, 20 defective. Nuri buys only if good. Find P(buys), P(doesn’t buy).
    Solution: Good=124. P(buys)=124/144=31/36. P(doesn’t buy)=20/144=5/36.
22. Q22. Two dice thrown. (i) Complete probability table for sums 2-12. (ii) Is claiming 11 equally-likely outcomes (each 1/11) correct?
    Solution: Total outcomes=36 (not 11). Sums 2..12 have 1,2,3,4,5,6,5,4,3,2,1 ways respectively (out of 36). (ii) Incorrect — the 11 sums are not equally likely.
23. Q23. Coin tossed 3 times; Hanif wins if all 3 match (HHH/TTT). Find P(Hanif loses).
    Solution: Total=8. Winning={HHH,TTT}=2. P(loses)=6/8=3/4.
24. Q24. A die thrown twice. Find P(5 doesn’t occur on either throw), P(5 occurs at least once).
    Solution: Total=36. Avoiding 5 both times=5×5=25 ⇒ 25/36. At least one 5=1-25/36=11/36.
25. Q25. Are these arguments correct? (i) Two coins give 3 outcomes so each has P=1/3. (ii) A die gives 2 outcomes (odd/even) so P(odd)=1/2.
    Solution: (i) Incorrect — actual outcomes are HH,HT,TH,TT (4), so P(2 heads)=1/4, P(1 each)=1/2. (ii) Correct (coincidentally) — die has 6 equally likely faces, 3 odd, so P(odd)=1/2.

More on This Chapter

• NCERT Solutions – Chapter 14
• Extra Questions (HOTS) – Chapter 14
• Revision Notes – Chapter 14
• Class 10 Maths Book (Catalog Page)

FAQ

Q: Is this content updated for the 2026-27 NCERT edition?
A: Yes. The current rationalised syllabus has only Exercise 14.1 (25 questions) — the older optional Exercise 14.2 has been removed, confirmed against three independent current sources.

Q: What’s the single most important formula in this chapter?
A: P(E) = (favourable outcomes)/(total outcomes), with 0≤P(E)≤1 and P(E)+P(not E)=1.

Written by Satish

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