Well-structured ICSE Class 10 Maths Solutions S Chand Chapter 20 Probability Ex 20(a) facilitate a deeper understanding of mathematical principles.
S Chand Class 10 ICSE Maths Solutions Chapter 20 Probability Ex 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
(1) You will throw a 7 with a normal die.
(2) Your friend will call you tonight.
(3) A cat will give birth to puppies next year.
(4) Thursday will be the day after Wednesday next week.
(5) You will have cornflakes, samosas and toasts in your breakfast today.
(6) It will be winter in Australia when it is summer in India.
(7) You will be able to see a live dinosaur in the city zoo.
(8) You will be awarded a prize for your good performance.
Solution:
(1) (b) as it has 1 to 6 numbers on it.
(2) (a) It may or may not, my friend call me.
(3) (b) as a cat gives birth to kitten not puppies
(4) (c) as every Thursday comes after Wednesday.
(5) (a) It may or may not that we get these things.
(6) (c) When it is summer in India which is in north hemisphere, it will be winter in Australia which is in south hemisphere of earth.
(7) (b) as a dinosaur is no more now.
(8) (a) It may or may not that I shall get a prize.
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.
Solution:
(1) (a) 1 may get or may not get reservation.
(2) (b) It is not yet possible to go to moon.
(3) (a) Generally, one or more students remain absent everyday.
(4) (a) There are chances that in January, it will fall snow in Mussorie which is situated on mountains.
(5) (b) As in month of March in Delhi, there are no heavy rains.
(6) (a) It may be or may not be me because an army officer.
Question 3.
Choose the likelihood which matches the outcome of each event :
(a) Impossible
(b) Unlikely
(c) Even Chance
(d) Likely
(e) Certain
(1) The school football team will win the local tournament.
(2) Mr. Shah will cut the grass on his lawn when it is snowing.
(3) While going to school, you will pass by a white car.
(4) The mountaineer will be hurt if he falls off the mountain.
(5) The number on the top face of an ordinary die will be an even number.
(6) The next baby to be born will be a female.
(7) The member on the top face of an ordinary die when rolled will be less than 7.
(8) The Titanic will float back up to the top of the ocean.
(9) You will live for 100 years.
(10) A dog will have kittens.
(11) Monday will be the day after Tuesday next week.
(12) You will have a birthday next year.
Solution:
(1) (c) There are chances to win the match.
(2) (a) It is not possible to cut the grass when it is snowing.
(3) (d) There are chances that we may pass by a white car.
(4) (e) It is certain that a mountaineer will be hurt on falling from a mountain.
(5) (c) It may or may not be possible to come an even number.
(6) (c) There are chances to be born next baby being a female.
(7) (e) A die has number from 1 to 6 which are less than 7.
(8) (a) It is not possible for the Titanic to float back.
(9) (b) There are rare chances to live up to 100 years age.
(10) (a) A dog bears to nothing.
(11) (a) Every Monday comes after Sunday but not after Tuesday.
(12) (d) If I may alive, it can be possible otherwise not.
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?
Solution:
We know that P (E) = \(\frac{\text { Number of favourable outcomes }}{\text { Number of possible outcomes }}\)
Here in the figure, there are 4 pink cards and 6 grey cards and in this way total cards are = 10
∴ Possible outcomes = 10, now
(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 = \(\frac { 1 }{ 10 }\)
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?
Solution:
We know that P (E) = \(\frac{\text { Number of favourable outcomes }}{\text { Number of possible outcomes }}\)
A 10-sided die is thrown which his numbers from 1 to 10 on it
∴ Possible outcomes = 10, now
(i) Probability of getting an integer = \(\frac { 10 }{ 10 }\) = 1 (∵ 1 to 10 are all integers)
(ii) Probability of getting a fractions = \(\frac { 0 }{ 10 }\) = 1 (∵ On the die, there is no fraction)
(iii) Probability of getting a number greater than 5 = \(\frac { 5 }{ 10 }\) = \(\frac { 1 }{ 2 }\) {6, 7, 8, 9, 10 are greater than 5}
(iv) Probability of getting a 5 = \(\frac { 1 }{ 10 }\)
(v) Probability of getting the numbers 1, 2, 3 or 4 = \(\frac { 4 }{ 10 }\) = \(\frac { 2 }{ 5 }\)
(vi) The sum of the probability 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