Class 9 Maths - Chapter 14 Question Answers Probability

 Page 1


  
              
      
  
                       
      
  
Q u e s t i o n : 1 5
Define a trial.
S o l u t i o n :
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
D e f i n i t i o n :
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is
called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to
differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the
combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there
are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5
trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as
tossing one coin 4 times.
Q u e s t i o n : 1 6
Define an elementary event.
S o l u t i o n :
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word
event means something that result.
D e f i n i t i o n :
Page 2


  
              
      
  
                       
      
  
Q u e s t i o n : 1 5
Define a trial.
S o l u t i o n :
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
D e f i n i t i o n :
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is
called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to
differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the
combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there
are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5
trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as
tossing one coin 4 times.
Q u e s t i o n : 1 6
Define an elementary event.
S o l u t i o n :
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word
event means something that result.
D e f i n i t i o n :
An elementary event is any single outcome of a trial. Elementary events are also called simple events.
To illustrate the definition, let us take examples:
1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an
elementary event.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an elementary event.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 7
Define an event.
S o l u t i o n :
What are the meanings of event?
The word event means something that result.
D e f i n i t i o n :
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome
like HH is called an event elementaryevent
. The collections like {HH, HT}, {HH, HT, TT} etc are all events compoundevent
.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an event elementaryevent
. The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events compoundevents
.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 8
Define probability of an event.
S o l u t i o n :
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when
repeating the experiment.
D e f i n i t i o n :
The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A
is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted
by and is given by
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of
trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the
probability of the event A is
Page 3


  
              
      
  
                       
      
  
Q u e s t i o n : 1 5
Define a trial.
S o l u t i o n :
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
D e f i n i t i o n :
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is
called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to
differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the
combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there
are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5
trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as
tossing one coin 4 times.
Q u e s t i o n : 1 6
Define an elementary event.
S o l u t i o n :
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word
event means something that result.
D e f i n i t i o n :
An elementary event is any single outcome of a trial. Elementary events are also called simple events.
To illustrate the definition, let us take examples:
1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an
elementary event.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an elementary event.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 7
Define an event.
S o l u t i o n :
What are the meanings of event?
The word event means something that result.
D e f i n i t i o n :
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome
like HH is called an event elementaryevent
. The collections like {HH, HT}, {HH, HT, TT} etc are all events compoundevent
.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an event elementaryevent
. The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events compoundevents
.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 8
Define probability of an event.
S o l u t i o n :
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when
repeating the experiment.
D e f i n i t i o n :
The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A
is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted
by and is given by
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of
trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the
probability of the event A is
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a
number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the
event A is
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 9
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is 
2
5
, find the number of red balls in the bag.
S o l u t i o n :
The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is .
Let A be the event of drawing a white ball.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
But, it is given that . So, we have
Hence the number of red balls is .
Q u e s t i o n : 2 0
A die is thrown 100 times. If the probability of getting an even number is 
2
5
Page 4


  
              
      
  
                       
      
  
Q u e s t i o n : 1 5
Define a trial.
S o l u t i o n :
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
D e f i n i t i o n :
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is
called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to
differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the
combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there
are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5
trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as
tossing one coin 4 times.
Q u e s t i o n : 1 6
Define an elementary event.
S o l u t i o n :
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word
event means something that result.
D e f i n i t i o n :
An elementary event is any single outcome of a trial. Elementary events are also called simple events.
To illustrate the definition, let us take examples:
1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an
elementary event.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an elementary event.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 7
Define an event.
S o l u t i o n :
What are the meanings of event?
The word event means something that result.
D e f i n i t i o n :
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome
like HH is called an event elementaryevent
. The collections like {HH, HT}, {HH, HT, TT} etc are all events compoundevent
.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an event elementaryevent
. The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events compoundevents
.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 8
Define probability of an event.
S o l u t i o n :
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when
repeating the experiment.
D e f i n i t i o n :
The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A
is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted
by and is given by
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of
trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the
probability of the event A is
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a
number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the
event A is
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 9
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is 
2
5
, find the number of red balls in the bag.
S o l u t i o n :
The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is .
Let A be the event of drawing a white ball.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
But, it is given that . So, we have
Hence the number of red balls is .
Q u e s t i o n : 2 0
A die is thrown 100 times. If the probability of getting an even number is 
2
5
. How many times an odd number is obtained?
S o l u t i o n :
The total number of trials is 100. Let the number of times an even number is obtained is x.
Let A be the event of getting an even number.
The number of times A happens is x.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
But, it is given that . So, we have
Hence an even number is obtained 40 times. Consequently, an odd number is obtained times.
Q u e s t i o n : 2 1
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
 
Outcome 3 heads 2 heads 1 head No head
Frequency 23 72 77 28
Find the probability of getting at most two heads.
S o l u t i o n :
The total number of trials is 200.
Let A be the event of getting at most two heads.
The number of times A happens is .
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
Q u e s t i o n : 2 2
In Q.No. 7, what is the probability of getting at least two heads?
S o l u t i o n :
Page 5


  
              
      
  
                       
      
  
Q u e s t i o n : 1 5
Define a trial.
S o l u t i o n :
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
D e f i n i t i o n :
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is
called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to
differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the
combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there
are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5
trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as
tossing one coin 4 times.
Q u e s t i o n : 1 6
Define an elementary event.
S o l u t i o n :
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word
event means something that result.
D e f i n i t i o n :
An elementary event is any single outcome of a trial. Elementary events are also called simple events.
To illustrate the definition, let us take examples:
1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an
elementary event.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an elementary event.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 7
Define an event.
S o l u t i o n :
What are the meanings of event?
The word event means something that result.
D e f i n i t i o n :
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome
like HH is called an event elementaryevent
. The collections like {HH, HT}, {HH, HT, TT} etc are all events compoundevent
.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is
called an event elementaryevent
. The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events compoundevents
.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 8
Define probability of an event.
S o l u t i o n :
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when
repeating the experiment.
D e f i n i t i o n :
The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A
is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted
by and is given by
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of
trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the
probability of the event A is
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a
number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the
event A is
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Q u e s t i o n : 1 9
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is 
2
5
, find the number of red balls in the bag.
S o l u t i o n :
The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is .
Let A be the event of drawing a white ball.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
But, it is given that . So, we have
Hence the number of red balls is .
Q u e s t i o n : 2 0
A die is thrown 100 times. If the probability of getting an even number is 
2
5
. How many times an odd number is obtained?
S o l u t i o n :
The total number of trials is 100. Let the number of times an even number is obtained is x.
Let A be the event of getting an even number.
The number of times A happens is x.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
But, it is given that . So, we have
Hence an even number is obtained 40 times. Consequently, an odd number is obtained times.
Q u e s t i o n : 2 1
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
 
Outcome 3 heads 2 heads 1 head No head
Frequency 23 72 77 28
Find the probability of getting at most two heads.
S o l u t i o n :
The total number of trials is 200.
Let A be the event of getting at most two heads.
The number of times A happens is .
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have .
Q u e s t i o n : 2 2
In Q.No. 7, what is the probability of getting at least two heads?
S o l u t i o n :
The total number of trials is 200.
Let A be the event of getting atleast two heads.
The number of times A happens is .
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials.
Then the empirical probability of happening of event A is denoted by and is given by
Therefore, we have