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# NCERT Solutions, Exercise 15.1: Probability, Class 10 (Mathematics) Class 10 Notes | EduRev

## Class 10 : NCERT Solutions, Exercise 15.1: Probability, Class 10 (Mathematics) Class 10 Notes | EduRev

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Exercise 15.1
Question 1:
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
_______.
(ii) The probability of an event that cannot happen is _________. Such
as event is called _________.
(iii) The probability of an event that is certain to happen is _________.
Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an
experiment is
_________.
(v) The probability of an event is greater than or equal to _______ and
less than or equal to _______.
(i) 1
(ii) 0, impossible event
(iii) 1, sure event or certain event
(iv) 1
(v) 0, 1
Question 2:
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.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot.
wrong.
(iv) A baby is born. It is a boy or a girl.

Page 2

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Exercise 15.1
Question 1:
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
_______.
(ii) The probability of an event that cannot happen is _________. Such
as event is called _________.
(iii) The probability of an event that is certain to happen is _________.
Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an
experiment is
_________.
(v) The probability of an event is greater than or equal to _______ and
less than or equal to _______.
(i) 1
(ii) 0, impossible event
(iii) 1, sure event or certain event
(iv) 1
(v) 0, 1
Question 2:
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.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot.
wrong.
(iv) A baby is born. It is a boy or a girl.

(Class – X)

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2

(i) It is not an equally likely event, as it depends on various factors such as
whether the car will start or not. And factors for both the conditions are not
the same.
(ii) It is not an equally likely event, as it depends on the player’s ability and
there is no information given about that.
(iii) It is an equally likely event.
(iv) It is an equally likely event.

Question 3:
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 game?
When we toss a coin, the possible outcomes are only two, head or tail, which
are equally likely outcomes. Therefore, the result of an individual toss is
completely unpredictable.

Question 4:
Which of the following cannot be the probability of an event?

Probability of an event (E) is always greater than or equal to 0. Also, it is
always less than or equal to one. This implies that the probability of an event
cannot be negative or greater than 1. Therefore, out of these alternatives,
-1.5 cannot be a probability of an event.
Hence, (B)

Question 5:
If P(E) = 0.05, what is the probability of ‘not E’?
We know that,
Page 3

(Class – X)

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Exercise 15.1
Question 1:
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
_______.
(ii) The probability of an event that cannot happen is _________. Such
as event is called _________.
(iii) The probability of an event that is certain to happen is _________.
Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an
experiment is
_________.
(v) The probability of an event is greater than or equal to _______ and
less than or equal to _______.
(i) 1
(ii) 0, impossible event
(iii) 1, sure event or certain event
(iv) 1
(v) 0, 1
Question 2:
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.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot.
wrong.
(iv) A baby is born. It is a boy or a girl.

(Class – X)

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2

(i) It is not an equally likely event, as it depends on various factors such as
whether the car will start or not. And factors for both the conditions are not
the same.
(ii) It is not an equally likely event, as it depends on the player’s ability and
there is no information given about that.
(iii) It is an equally likely event.
(iv) It is an equally likely event.

Question 3:
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 game?
When we toss a coin, the possible outcomes are only two, head or tail, which
are equally likely outcomes. Therefore, the result of an individual toss is
completely unpredictable.

Question 4:
Which of the following cannot be the probability of an event?

Probability of an event (E) is always greater than or equal to 0. Also, it is
always less than or equal to one. This implies that the probability of an event
cannot be negative or greater than 1. Therefore, out of these alternatives,
-1.5 cannot be a probability of an event.
Hence, (B)

Question 5:
If P(E) = 0.05, what is the probability of ‘not E’?
We know that,
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Therefore, the probability of ‘not E’ is 0.95.
Question 6:
A bag contains lemon flavoured candies only. Malini takes out one candy
without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy?
(ii) a lemon flavoured candy?
(i) The bag contains lemon flavoured candies only. It does not contain any
orange flavoured candies. This implies that every time, she will take out
only lemon flavoured candies. Therefore, event that Malini will take out an
orange flavoured candy is an impossible event.
Hence, P (an orange flavoured candy) = 0
(ii) As the bag has lemon flavoured candies, Malini will take out only lemon
flavoured candies. Therefore, event that Malini will take out a lemon
flavoured candy is a sure event.
P (a lemon flavoured candy) = 1
Question 7:
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?
Probability that two students are not having same birthday P ( ) = 0.992
Page 4

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Exercise 15.1
Question 1:
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
_______.
(ii) The probability of an event that cannot happen is _________. Such
as event is called _________.
(iii) The probability of an event that is certain to happen is _________.
Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an
experiment is
_________.
(v) The probability of an event is greater than or equal to _______ and
less than or equal to _______.
(i) 1
(ii) 0, impossible event
(iii) 1, sure event or certain event
(iv) 1
(v) 0, 1
Question 2:
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.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot.
wrong.
(iv) A baby is born. It is a boy or a girl.

(Class – X)

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2

(i) It is not an equally likely event, as it depends on various factors such as
whether the car will start or not. And factors for both the conditions are not
the same.
(ii) It is not an equally likely event, as it depends on the player’s ability and
there is no information given about that.
(iii) It is an equally likely event.
(iv) It is an equally likely event.

Question 3:
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 game?
When we toss a coin, the possible outcomes are only two, head or tail, which
are equally likely outcomes. Therefore, the result of an individual toss is
completely unpredictable.

Question 4:
Which of the following cannot be the probability of an event?

Probability of an event (E) is always greater than or equal to 0. Also, it is
always less than or equal to one. This implies that the probability of an event
cannot be negative or greater than 1. Therefore, out of these alternatives,
-1.5 cannot be a probability of an event.
Hence, (B)

Question 5:
If P(E) = 0.05, what is the probability of ‘not E’?
We know that,
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Therefore, the probability of ‘not E’ is 0.95.
Question 6:
A bag contains lemon flavoured candies only. Malini takes out one candy
without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy?
(ii) a lemon flavoured candy?
(i) The bag contains lemon flavoured candies only. It does not contain any
orange flavoured candies. This implies that every time, she will take out
only lemon flavoured candies. Therefore, event that Malini will take out an
orange flavoured candy is an impossible event.
Hence, P (an orange flavoured candy) = 0
(ii) As the bag has lemon flavoured candies, Malini will take out only lemon
flavoured candies. Therefore, event that Malini will take out a lemon
flavoured candy is a sure event.
P (a lemon flavoured candy) = 1
Question 7:
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?
Probability that two students are not having same birthday P ( ) = 0.992
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Probability that two students are having same birthday P (E) = 1 - P ( )
= 1 - 0.992
= 0.008

Question 8:
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from
the bag.
What is the probability that the ball drawn is (i) red? (ii) not red?
(i) Total number of balls in the bag = 8

(ii) Probability of not getting red ball
= 1 - Probability of getting a red ball

Question 9:
A box contains 5 red marbles, 8 white marbles and 4 green marbles. One
marble is taken out of the box at random. What is the probability that the
marble taken out will be (i) red? (ii) white? (iii) not green?
Total number of marbles = 5 + 8 + 4
= 17
(i) Number of red marbles = 5
Page 5

(Class – X)

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1

Exercise 15.1
Question 1:
Complete the following statements:
(i) Probability of an event E + Probability of the event ‘not E’ =
_______.
(ii) The probability of an event that cannot happen is _________. Such
as event is called _________.
(iii) The probability of an event that is certain to happen is _________.
Such as event is called ________.
(iv) The sum of the probabilities of all the elementary events of an
experiment is
_________.
(v) The probability of an event is greater than or equal to _______ and
less than or equal to _______.
(i) 1
(ii) 0, impossible event
(iii) 1, sure event or certain event
(iv) 1
(v) 0, 1
Question 2:
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.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot.
wrong.
(iv) A baby is born. It is a boy or a girl.

(Class – X)

A Free web support in Education

2

(i) It is not an equally likely event, as it depends on various factors such as
whether the car will start or not. And factors for both the conditions are not
the same.
(ii) It is not an equally likely event, as it depends on the player’s ability and
there is no information given about that.
(iii) It is an equally likely event.
(iv) It is an equally likely event.

Question 3:
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 game?
When we toss a coin, the possible outcomes are only two, head or tail, which
are equally likely outcomes. Therefore, the result of an individual toss is
completely unpredictable.

Question 4:
Which of the following cannot be the probability of an event?

Probability of an event (E) is always greater than or equal to 0. Also, it is
always less than or equal to one. This implies that the probability of an event
cannot be negative or greater than 1. Therefore, out of these alternatives,
-1.5 cannot be a probability of an event.
Hence, (B)

Question 5:
If P(E) = 0.05, what is the probability of ‘not E’?
We know that,
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Therefore, the probability of ‘not E’ is 0.95.
Question 6:
A bag contains lemon flavoured candies only. Malini takes out one candy
without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy?
(ii) a lemon flavoured candy?
(i) The bag contains lemon flavoured candies only. It does not contain any
orange flavoured candies. This implies that every time, she will take out
only lemon flavoured candies. Therefore, event that Malini will take out an
orange flavoured candy is an impossible event.
Hence, P (an orange flavoured candy) = 0
(ii) As the bag has lemon flavoured candies, Malini will take out only lemon
flavoured candies. Therefore, event that Malini will take out a lemon
flavoured candy is a sure event.
P (a lemon flavoured candy) = 1
Question 7:
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?
Probability that two students are not having same birthday P ( ) = 0.992
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Probability that two students are having same birthday P (E) = 1 - P ( )
= 1 - 0.992
= 0.008

Question 8:
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from
the bag.
What is the probability that the ball drawn is (i) red? (ii) not red?
(i) Total number of balls in the bag = 8

(ii) Probability of not getting red ball
= 1 - Probability of getting a red ball

Question 9:
A box contains 5 red marbles, 8 white marbles and 4 green marbles. One
marble is taken out of the box at random. What is the probability that the
marble taken out will be (i) red? (ii) white? (iii) not green?
Total number of marbles = 5 + 8 + 4
= 17
(i) Number of red marbles = 5
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(ii) Number of white marbles = 8

(iii) Number of green marbles = 4

Question 10:
A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2
coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall
out when the bank is turned upside down, what is the probability that the
coin
(i) Will be a 50 p coin?
(ii) Will not be a Rs.5 coin?
Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180
Probability of not getting a green marble

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