| --- |
| 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 β€ P(E) β€ 1 |
| P(E) + P(EΜ
) = 1 (EΜ
= 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 ___. β 0,1. β
|
| |
| 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. β
|
| |
| 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. β
|
| |
| Q4. A piggy bank has 100βΉ1, 50βΉ2, 20βΉ5 and 10βΉ10 coins. A coin withdrawn at random. Find P(βΉ5 coin). |
| Answer: Total=180. P=20/180=1/9. β
|
| |
| 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. β
|
| |
| Q6. A lot contains 144 ball pens, 20 defective. Find P(good pen). |
| Answer: Good=124. P=124/144=31/36. β
|
| |
| 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. β
|
| |
| 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. β
|
| |
| Q9. A child has a die with numbers 1-6. Find P(number less than 3). |
| Answer: {1,2}. P=2/6=1/3. β
|
| |
| 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)=2Γ5/(x+5) β x=10. β
|
| |
| 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. β
|
| (ii) Doublets: (1,1),(2,2),...,(6,6). P=6/36=1/6. β
|
| (iii) Sum<5: (1,1),(1,2),(2,1),(1,3),(3,1),(2,2). P=6/36=1/6. β
|
| (iv) Sum>10: (5,6),(6,5),(6,6). P=3/36=1/12. β
|
| (v) 5 on at least one: (5,1)...(5,6),(1,5)...(4,5),(6,5)=11 outcomes. P=11/36. β
|
| |
| 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. β
|
| |
| 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). β
|
| |
| 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)=4/9Γ4/9=16/81. β
|
| |
| Q15. Probability of selecting a rotten apple from 900 is 0.18. How many rotten apples? |
| Answer: 0.18Γ900=162 rotten apples. β
|
| |
| Q16. A jar has 24 marbles: some green, others blue. P(green)=2/3. Find number of blue marbles. |
| Answer: Green=2/3Γ24=16. Blue=24-16=8. β
|
