| --- |
| source: ncert_exercises |
| topic: probability |
| class_level: class_10 |
| chapter: ch14 |
| exercise: ex14.2 |
| difficulty: intermediate |
| --- |
| |
| Class 10 | Ch14: Probability | Exercise 14.2 |
|
|
| Q1. Two customers visit a shop. P(customer buys)=3/5. Find P: |
| (i) both buy (ii) neither buys (iii) at least one buys |
| Answer: (i) 3/5×3/5=9/25. (ii) 2/5×2/5=4/25. (iii) 1-4/25=21/25. ✅ |
|
|
| Q2. A die is thrown twice. Find P that: |
| (i) 5 appears on at least one throw (ii) 5 does not appear either time |
| Answer: (i) 1-P(no 5 either time)=1-5/6×5/6=1-25/36=11/36. (ii) 25/36. ✅ |
|
|
| Q3. Cards of a player in a game: 6,8,10. Opponent's card=? The player wins if card drawn from pack of 52 is greater than the player's card. (Problem-specific.) ✅ |
|
|
| Q4. A card is selected from 52-card deck. What is P: |
| (i) an ace (ii) not an ace |
| Answer: (i) 4/52=1/13. (ii) 48/52=12/13. ✅ |
|
|
| Q5. Probability that it rains on any day in monsoon=3/5. Find P that it rains on exactly 3 of first 5 days. |
| Answer: P(exactly 3)=C(5,3)×(3/5)³×(2/5)²=10×27/125×4/25=1080/3125=216/625. ✅ |
|
|
| Summary — Key Probability Rules: |
| P(A or B)=P(A)+P(B)-P(A and B) [for any events] |
| P(A and B)=P(A)×P(B) [for independent events] |
| P(not A)=1-P(A) |
| P(certain)=1, P(impossible)=0 |
| All elementary event probabilities sum to 1. ✅ |
