knowledge-base/class_10/ch14/0199_probability.md

metadata

source: ncert_exercises
topic: probability
class_level: class_10
chapter: ch14
exercise: ex14.1
difficulty: intermediate

Class 10 | Ch14: Probability | Exercise 14.1

Probability = Number of favourable outcomes / Total number of possible outcomes P(E) = n(E)/n(S)

Key rules: 0 ≤ P(E) ≤ 1 P(E) + P(E̅) = 1 (E̅ = complement of E) Certain event: P=1. Impossible event: P=0.

Q1. Complete the statements: (i) Probability of event that cannot happen = 0. (ii) Probability of event that is certain to happen = 1. (iii) Sum of probabilities of all elementary events of an experiment = 1. (iv) Probability of an event is greater than or equal to ___ and less than or equal to ___. → 0,1. ✅

Q2. A bag has 3 red and 5 black balls. Ball is drawn at random. Find probability it is: (i) red (ii) not red Answer: Total=8. (i) P(red)=3/8. (ii) P(not red)=5/8. ✅

Q3. A box contains 5 red, 8 orange, 4 green marbles. One marble drawn at random. Find: (i) P(red) (ii) P(not green) Answer: Total=17. (i) 5/17. (ii) 13/17. ✅

Q4. A piggy bank has 100₹1, 50₹2, 20₹5 and 10₹10 coins. A coin withdrawn at random. Find P(₹5 coin). Answer: Total=180. P=20/180=1/9. ✅

Q5. Gopi buys a fish from a shop with 5 tiger fish and 20 other fish. Find P(tiger fish). Answer: P=5/25=1/5. ✅

Q6. A lot contains 144 ball pens, 20 defective. Find P(good pen). Answer: Good=124. P=124/144=31/36. ✅

Q7. (i) 12 defective pens from 132. Find P(not defective). P=120/132=10/11. (ii) Five cards: king of diamonds, queen of hearts, jack of spades, 10,9 of hearts. One card selected. Find: P(king), P(queen of hearts), P(a face card), P(10 of spades). Answer: (ii) P(king)=1/5. P(queen of hearts)=1/5. P(face card)=3/5. P(10 of spades)=0. ✅

Q8. Cards 3,4,5,6,7,8,9 in a bag. One drawn at random. Find: (i) P(prime number) (ii) P(less than 5) (iii) P(odd number > 5) Answer: (i) Primes: 3,5,7. P=3/7. (ii) Less than 5: 3,4. P=2/7. (iii) Odd>5: 7,9. P=2/7. ✅

Q9. A child has a die with numbers 1-6. Find P(number less than 3). Answer: {1,2}. P=2/6=1/3. ✅

Q10. A bag has 5 red balls and some blue balls. P(blue ball) = twice P(red ball). Find number of blue balls. Answer: Let blue=x. P(red)=5/(x+5), P(blue)=x/(x+5). x/(x+5)=2×5/(x+5) → x=10. ✅

Q11. Two dice thrown simultaneously. Find P: (i) sum 8 (ii) doublets (iii) sum<5 (iv) sum>10 (v) 5 on at least one die Answer: Total outcomes=36. (i) Pairs summing 8: (2,6),(3,5),(4,4),(5,3),(6,2). P=5/36. ✅ (ii) Doublets: (1,1),(2,2),...,(6,6). P=6/36=1/6. ✅ (iii) Sum<5: (1,1),(1,2),(2,1),(1,3),(3,1),(2,2). P=6/36=1/6. ✅ (iv) Sum>10: (5,6),(6,5),(6,6). P=3/36=1/12. ✅ (v) 5 on at least one: (5,1)...(5,6),(1,5)...(4,5),(6,5)=11 outcomes. P=11/36. ✅

Q12. A card is drawn from 52-card deck. Find P: (i) a king of red colour (ii) a face card (iii) red face card (iv) jack of spades (v) queen of diamonds (vi) card is neither king nor queen Answer: (i) 2/52=1/26. (ii) 12/52=3/13. (iii) 6/52=3/26. (iv) 1/52. (v) 1/52. (vi) 44/52=11/13. ✅

Q13. Five cards: ten,jack,queen,king,ace of spades. Well-shuffled. One card picked. Find: (i) P(queen) (ii) P(an ace) (iii) P(a face card) Answer: (i) 1/5. (ii) 1/5. (iii) 3/5 (jack, queen, king). ✅

Q14. A box has 4 white,3 blue,2 red balls. Ball drawn, colour noted, replaced. Next ball drawn. Find P both selected balls are white. Answer: P(white both)=4/9×4/9=16/81. ✅

Q15. Probability of selecting a rotten apple from 900 is 0.18. How many rotten apples? Answer: 0.18×900=162 rotten apples. ✅

Q16. A jar has 24 marbles: some green, others blue. P(green)=2/3. Find number of blue marbles. Answer: Green=2/3×24=16. Blue=24-16=8. ✅