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. ✅