OP Malhotra Class 10 Maths Solutions Chapter 20 Probability Exercise 20 (A)

Question 1. In the following events, match correctly to indicate whether the outcomes are possible, certain, or impossible.
(a) Possible
(b) Impossible
(c) Certain
Answer:
(1) Rolling a 7 with a normal die: (b) Impossible
Explanation: A standard die has numbers from 1 to 6. Therefore, rolling a 7 is not possible.
(2) Your friend will call you tonight: (a) Possible
Explanation: Your friend might call you, or they might not. There is a chance this could happen.
(3) A cat will give birth to puppies next year: (b) Impossible
Explanation: Cats give birth to kittens, not puppies. This event cannot happen biologically.
(4) Thursday will be the day after Wednesday next week: (c) Certain
Explanation: Thursday always follows Wednesday in the sequence of days. This is a definite fact.
(5) You will have cornflakes, samosas and toasts in your breakfast today: (a) Possible
Explanation: You might have all those food items for breakfast, or you might have something else. It is not guaranteed, but it is possible.
(6) It will be winter in Australia when it is summer in India: (c) Certain
Explanation: When India, which is in the Northern Hemisphere, has summer, Australia, which is in the Southern Hemisphere, will always experience winter. The seasons are opposite in different hemispheres.
(7) You will be able to see a live dinosaur in the city zoo: (b) Impossible
Explanation: Dinosaurs are extinct and do not exist anymore. So, you cannot see a live one in a zoo.
(8) You will be awarded a prize for your good performance: (a) Possible
Explanation: You might receive a prize for good performance, or you might not. It depends on various factors and competitions.
In simple words: For each event, decide if it definitely will happen (certain), definitely won't happen (impossible), or might happen (possible). Look at the facts to make your choice.

🎯 Exam Tip: When matching events to likelihoods, think about whether the event is based on a fixed rule, a natural law, or simply a chance occurrence. This helps determine if it's certain, impossible, or merely possible.

Question 2. Categorize each outcome as likely or unlikely, (a) Likely (b) Unlikely
(1) You will not get reservation in the train due to heavy Dusshera rush.
(2) Your friend will go to moon next month.
(3) Someone in your class will be absent next week.
(4) It will snow in Mussorie in January.
(5) There will be floods in Delhi in March next year.
(6) You will become an army officer when you grow up.
Answer:
(1) You will not get reservation in the train due to heavy Dusshera rush: (a) Likely
Explanation: During a heavy Dusshera rush, many people travel. So, it is likely that you might not get a train reservation.
(2) Your friend will go to moon next month: (b) Unlikely
Explanation: Currently, it is not common or easy for an ordinary person to travel to the moon. Therefore, it is unlikely.
(3) Someone in your class will be absent next week: (a) Likely
Explanation: It is common for students to miss school sometimes due to various reasons. So, it is likely that someone will be absent next week.
(4) It will snow in Mussorie in January: (a) Likely
Explanation: Mussoorie is a hill station known for snowfall in January. So, it is likely to snow there.
(5) There will be floods in Delhi in March next year: (b) Unlikely
Explanation: Delhi does not usually experience heavy rains or floods in March. Therefore, floods are unlikely at that time of year.
(6) You will become an army officer when you grow up: (a) Likely
Explanation: Becoming an army officer is a goal that can be achieved through hard work and meeting requirements. It is likely if you pursue it.
In simple words: Look at each event and decide if it usually happens or if it is rare. If it happens often, it's likely. If it rarely happens, it's unlikely.

🎯 Exam Tip: For "likely" vs "unlikely" questions, consider general trends, common occurrences, and known facts. What normally happens in a given situation helps determine the probability.

Question 3. Choose the likelihood which matches the outcome of each event :
(a) Impossible
(b) Unlikely
(c) Even Chance
(d) Likely
(e) Certain
Answer:
(1) The school football team will win the local tournament: (c) Even Chance
Explanation: In a tournament, a team has an even chance of winning or losing, as the outcome depends on performance against other teams.
(2) Mr. Shah will cut the grass on his lawn when it is snowing: (a) Impossible
Explanation: It is not possible to cut grass when it is covered in snow. This act would be impossible due to weather conditions.
(3) While going to school, you will pass by a white car: (d) Likely
Explanation: White cars are very common on the road. It is likely that you will see at least one white car on your way to school.
(4) The mountaineer will be hurt if he falls off the mountain: (e) Certain
Explanation: Falling from a mountain height will definitely cause injury. There is no doubt about this outcome.
(5) The number on the top face of an ordinary die will be an even number: (c) Even Chance
Explanation: A standard die has three even numbers (2, 4, 6) and three odd numbers (1, 3, 5). So, getting an even number has an equal or even chance.
(6) The next baby to be born will be a female: (c) Even Chance
Explanation: The probability of a baby being born male or female is roughly equal. Thus, there is an even chance for a female.
(7) The member on the top face of an ordinary die when rolled will be less than 7: (e) Certain
Explanation: A standard die only has numbers from 1 to 6. All these numbers are less than 7, so it is certain to roll a number less than 7.
(8) The Titanic will float back up to the top of the ocean: (a) Impossible
Explanation: The Titanic sank over a century ago and is now at the bottom of the ocean. It is impossible for it to float back up.
(9) You will live for 100 years: (b) Unlikely
Explanation: While possible, very few people live to be 100 years old. So, it is generally considered an unlikely event.
(10) A dog will have kittens: (a) Impossible
Explanation: Dogs give birth to puppies, not kittens. Kittens are born to cats. This is a biological impossibility.
(11) Monday will be the day after Tuesday next week: (a) Impossible
Explanation: Monday always follows Sunday, not Tuesday. It is impossible for Monday to be the day after Tuesday.
(12) You will have a birthday next year: (d) Likely
Explanation: Everyone has a birthday once a year. It is highly likely that you will have one next year unless something unforeseen occurs.
In simple words: Match how likely each event is to one of the five options: impossible (cannot happen), unlikely (probably won't happen), even chance (could go either way), likely (probably will happen), or certain (definitely will happen).

🎯 Exam Tip: When evaluating events, distinguish between 'impossible' and 'unlikely'. Impossible means it absolutely cannot happen, while unlikely means it is very rare but still theoretically possible.

Question 4. Each of the cards pictured at the right is associated with a number and a colour as shown, and each is equally likely to be picked in a draw. If a card is drawn, what is the probability that the card :
(i) is pink?
(ii) is grey?
(iii) has a "1"?
(iv) has a "4"?
(v) has an "8"?
(vi) has a "9"?
(vii) has a numeral for a number less than 9?
(viii) has a numeral for an even number?
(ix) has a numeral for an odd number?
(x) has a “1” and is pink?
(xi) has a “2” and is pink?
Answer:
We know that Probability of an Event \( P(E) = \frac{\text { Number of favourable outcomes }}{\text { Number of possible outcomes }} \)
From the figure, there are 4 pink cards and 6 grey cards, making a total of 10 cards.
Total possible outcomes = 10.
(i) Probability of being a pink card = \( \frac { 4 }{ 10 } = \frac { 2 }{ 5 } \)
(ii) Probability of being a grey card = \( \frac { 6 }{ 10 } = \frac { 3 }{ 5 } \)
(iii) Probability of card which has a '1' = \( \frac { 2 }{ 10 } = \frac { 1 }{ 5 } \)
(iv) Probability of card which has '4' = \( \frac { 1 }{ 10 } \)
(v) Probability of card which has '8' = \( \frac { 1 }{ 10 } \)
(vi) Probability of card which has '9' = \( 0 \) (as there is no '9' in the card)
(vii) Probability of card which has numeral for a number less than 9 = \( \frac { 10 }{ 10 } = 1 \)
(viii) Probability of card which has a numeral for an even number = \( \frac { 5 }{ 10 } = \frac { 1 }{ 2 } \) (Even numbers are 2, 2, 4, 6, 8)
(ix) Probability of a card which has a numeral for an odd number = \( \frac { 5 }{ 10 } = \frac { 1 }{ 2 } \) (Odd numbers are 1, 1, 3, 5, 7)
(x) Probability of a card which has a '1' and is pink = \( \frac { 2 }{ 10 } = \frac { 1 }{ 5 } \)
(xi) Probability of a card which has '2' and is pink = \( \frac { 1 }{ 10 } \)
In simple words: To find the probability, count how many cards fit the description (favourable outcomes) and divide that by the total number of cards (total possible outcomes). Simplify the fraction if you can.

🎯 Exam Tip: Always clearly count the total number of items and the number of items that fit the specific condition. Double-check your counts for each sub-part, especially when dealing with multiple conditions like "number and color."

Question 5. A 10-sided die is thrown. What is the probability :
(i) of getting an integer?
(ii) of getting a fraction?
(iii) of getting a number greater than 5?
(iv) of getting a 5?
(v) of getting the numbers 1, 2, 3 or 4?
(vi) What is the sum of the probabilities obtained in (iii) to (v) above?
Answer:
We know that Probability of an Event \( P(E) = \frac{\text { Number of favourable outcomes }}{\text { Number of possible outcomes }} \)
A 10-sided die has numbers from 1 to 10 on it.
Total possible outcomes = 10.
(i) Probability of getting an integer = \( \frac { 10 }{ 10 } = 1 \) (Numbers 1 to 10 are all integers). All numbers on a die are whole numbers.
(ii) Probability of getting a fraction = \( \frac { 0 }{ 10 } = 0 \) (There are no fractions on the die). A die will never show a fraction.
(iii) Probability of getting a number greater than 5 = \( \frac { 5 }{ 10 } = \frac { 1 }{ 2 } \) (Numbers 6, 7, 8, 9, 10 are greater than 5). There are five numbers larger than 5.
(iv) Probability of getting a 5 = \( \frac { 1 }{ 10 } \). Only one face shows the number 5.
(v) Probability of getting the numbers 1, 2, 3 or 4 = \( \frac { 4 }{ 10 } = \frac { 2 }{ 5 } \). These are four specific numbers.
(vi) The sum of the probabilities obtained in (iii) to (v) above = \( \frac { 1 }{ 2 } + \frac { 1 }{ 10 } + \frac { 2 }{ 5 } = \frac { 5 }{ 10 } + \frac { 1 }{ 10 } + \frac { 4 }{ 10 } = \frac { 10 }{ 10 } = 1 \). When you add up the probabilities of these specific events, they total one.
In simple words: For a 10-sided die, count how many sides match the requirement for each question and divide by 10. For the last part, just add the fractions you found for parts (iii), (iv), and (v).

🎯 Exam Tip: Remember that the sum of probabilities for all possible outcomes of an event must always equal 1. When dealing with fractions, ensure you use a common denominator to add them correctly.