Ch 14: Probability (Part 1)
Based on the latest CBSE syllabus. Master the fundamentals of Probability: Coins, Balls, and Sure/Impossible events.
Exercise 14.1 (Questions 1 to 6)
💡 Concept: Probability of an event E + Probability of the event 'not E' = 1. i.e., P(E) + P(not E) = 1.
Q1. Complete the following statements:
- (i) Probability of an event E + Probability of the event 'not E' = 1.
- (ii) The probability of an event that cannot happen is 0. Such an event is called an impossible event.
- (iii) The probability of an event that is certain to happen is 1. Such an event is called a sure or certain event.
- (iv) The sum of the probabilities of all the elementary events of an experiment is 1.
- (v) The probability of an event is greater than or equal to 0 and less than or equal to 1.
Q2. Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
Not equally likely. The car usually starts unless it has a defect.
(ii) A player attempts to shoot a basketball. She/he shoots or misses.
Not equally likely. It depends on the player's skill.
(iii) A trial is made to answer a true-false question. The answer is right or wrong.
Equally likely. There are only two possible outcomes with equal chances.
(iv) A baby is born. It is a boy or a girl.
Equally likely. Both outcomes are biologically 50-50.
Q3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football match?
Solution:
When we toss a coin, the possible outcomes are only 'Head' or 'Tail'. These outcomes are equally likely, meaning the result is completely unpredictable and fair to both teams.
Q4. Which of the following cannot be the probability of an event?
Options: (A) 2/3 (B) -1.5 (C) 15% (D) 0.7
(B) -1.5 is the correct answer. Probability can never be negative. It always lies between 0 and 1.
Q5. If P(E) = 0.05, what is the probability of 'not E'?
Solution:
We know that P(E) + P(not E) = 1.
0.05 + P(not E) = 1
P(not E) = 1 - 0.05 = 0.95.
Q6. A bag contains lemon flavoured candies only. Malini takes out one candy without looking. What is the probability that she takes out: (i) an orange flavoured candy? (ii) a lemon flavoured candy?
(i) Orange flavoured candy: Since the bag contains ONLY lemon candies, getting an orange candy is an impossible event. Probability = 0.
(ii) Lemon flavoured candy: Since all candies are lemon, getting a lemon candy is a sure event. Probability = 1.
Exercise 14.1 (Questions 7 to 12)
Q7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Solution:
Let E be the event that 2 students have the same birthday.
P(not E) = 0.992
P(E) = 1 - P(not E) = 1 - 0.992 = 0.008.
Q8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random. What is the probability that the ball drawn is (i) red? (ii) not red?
Solution:
Total number of balls = 3 (red) + 5 (black) = 8.
(i) P(red) = Favorable outcomes / Total outcomes = 3/8.
(ii) P(not red) = 1 - P(red) = 1 - 3/8 = 5/8. (Or simply, number of black balls / Total = 5/8).
Q9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out. What is the probability that it will be (i) red? (ii) white? (iii) not green?
Solution:
Total marbles = 5 + 8 + 4 = 17.
(i) P(red) = 5 / 17
(ii) P(white) = 8 / 17
(iii) P(not green) = P(red or white) = (5 + 8) / 17 = 13 / 17
Q10. A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. What is the probability that the coin falling out will be (i) a 50p coin? (ii) will not be a ₹5 coin?
Solution:
Total coins = 100 + 50 + 20 + 10 = 180.
(i) Favorable outcomes for 50p = 100.
P(50p) = 100 / 180 = 5/9.
(ii) Number of coins that are NOT ₹5 = 180 - 10 = 170.
P(not ₹5) = 170 / 180 = 17/18.
Q11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish. What is the probability that the fish taken out is a male fish?
Solution:
Total fish = 5 + 8 = 13.
Number of male fish = 5.
P(male fish) = 5 / 13.
Q12. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at (i) 8? (ii) an odd number? (iii) a number greater than 2? (iv) a number less than 9?
Solution:
Total possible outcomes = 8.
(i) P(pointing at 8) = 1 / 8.
(ii) Odd numbers are 1, 3, 5, 7 (Total 4). P(odd number) = 4 / 8 = 1 / 2.
(iii) Numbers greater than 2 are 3, 4, 5, 6, 7, 8 (Total 6). P(> 2) = 6 / 8 = 3 / 4.
(iv) All numbers are less than 9 (Total 8). P(< 9) = 8 / 8 = 1 (Sure Event).