Points to Remember: Probability

``` Page 1

Probability
Page 2

Probability
Equally likely events :
Outcomes of an event are said to be
‘equally likely’ when they have the same chance of occurring.
Ex:    Rolling a die
Outcomes : 1, 2, 3, 4, 5 & 6. (All are equally likely to occur)
Impossible event : An event has no chance of occurrence ;
P ( Impossible event ) = 0
Ex: Getting the number 7 in a single roll of a die.
P( Getting 7 in a roll of a die ) = 0
Sure event : An event that has 100% chance of occurrence.
P ( sure event ) = 1
Ex: Getting number less than 7 in a single roll of a die.
P ( getting number less than 7 ) = 1
Mutually exclusive events ( Disjoint events ) :
Events A and B are said to be mutually exclusive if they do not have
any common point.
S = { 1, 2, 3, 4, 5, 6 }
A = { 4 } and B = { 1, 3, 5 }
A n B = ( empty set )
4
2
6
5
B
S
A
3
Exhaustive events : Two or more than two events
are said to be exhaustive events if their union is a sample space.
Ex: S = { 1, 2, 3, 4, 5, 6 }
A = { 3, 4, 5, 6 } and
B = { 1, 2, 3 }
A
n
B = { 1, 2, 3, 4, 5, 6 }
4
6
5
A
B
3
1
2
Complement events : Complementary events are those events
where probabilities of occurrence of one event exclude the
occurrence of the other.
Example :
Event (E)  -  Getting a head
Event (E)  -  Not getting a head (H) or Getting a tail (T)
P (E) = 1 - P (E)          OR        P (E) + P (E) = 1
Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
It is classied into two categories:
Experimental or Empirical Probability
A probability is based on the outcome of an actual experiment &
adequate recording of the happening of an event.
A probability is based on the assumption about the outcome of an
event (E) rather than the outcome of an actual experiment.
In Probability theory, an event is a set of outcomes of an experiment to which a probability is assigned.
Theoretical or Classical Probability
< 7
Odd
Even
H T
PROBABILITY 35
Probability
Page 3

Probability
Equally likely events :
Outcomes of an event are said to be
‘equally likely’ when they have the same chance of occurring.
Ex:    Rolling a die
Outcomes : 1, 2, 3, 4, 5 & 6. (All are equally likely to occur)
Impossible event : An event has no chance of occurrence ;
P ( Impossible event ) = 0
Ex: Getting the number 7 in a single roll of a die.
P( Getting 7 in a roll of a die ) = 0
Sure event : An event that has 100% chance of occurrence.
P ( sure event ) = 1
Ex: Getting number less than 7 in a single roll of a die.
P ( getting number less than 7 ) = 1
Mutually exclusive events ( Disjoint events ) :
Events A and B are said to be mutually exclusive if they do not have
any common point.
S = { 1, 2, 3, 4, 5, 6 }
A = { 4 } and B = { 1, 3, 5 }
A n B = ( empty set )
4
2
6
5
B
S
A
3
Exhaustive events : Two or more than two events
are said to be exhaustive events if their union is a sample space.
Ex: S = { 1, 2, 3, 4, 5, 6 }
A = { 3, 4, 5, 6 } and
B = { 1, 2, 3 }
A
n
B = { 1, 2, 3, 4, 5, 6 }
4
6
5
A
B
3
1
2
Complement events : Complementary events are those events
where probabilities of occurrence of one event exclude the
occurrence of the other.
Example :
Event (E)  -  Getting a head
Event (E)  -  Not getting a head (H) or Getting a tail (T)
P (E) = 1 - P (E)          OR        P (E) + P (E) = 1
Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
It is classied into two categories:
Experimental or Empirical Probability
A probability is based on the outcome of an actual experiment &
adequate recording of the happening of an event.
A probability is based on the assumption about the outcome of an
event (E) rather than the outcome of an actual experiment.
In Probability theory, an event is a set of outcomes of an experiment to which a probability is assigned.
Theoretical or Classical Probability
< 7
Odd
Even
H T
PROBABILITY 35
Probability
}
{
n (S) = 12
Throwing a die and a coin
(H,1), (H,2), (H,3), (H,4), (H,5), (H,6)
(T,1), (T ,2), (T ,3), (T ,4), (T ,5), (T ,6)
n (S) = a
n
a - number of possible
outcomes of an event
n - number of events
n (A) - number of elements of an event A
n (S) - number of elements in Sample
Space
n (A)
n (S)
p (A) =
Sample Space
Tossing coins Rolling dice
Drawing cards
A coin
{
H, T
[ n (S) = 2
n
] [ n (S) = 6
n
] [ n (S) = 52 ]
2
1
6
1
2
2 6
2
2
3
}
n (S) = 2
T wo coins
{
HH, HT, TH, TT
}
n (S) = 4
Three coins
{ HHH, HHT, HTH, THH,
TTT, THT, HTT, TTH }
n (S) = 8
A die
{1, 2, 3, 4, 5, 6 }
n (S) = 6
Two dice
{ (1,1), (1,2), .......(1,6)
(2,1), ................(2,6)
............................
............................
............................
(6,1), ................(6,6)
}
n (S) = 36
Black / Red
n (A) = 26
Ace/ King/ Queen/
Jack/ Any number
n (A) = 4
Any Shape
n (A) = 13
A Face card
n (A) = 12
/ / /
Introduction to probability Ball and Card experiment and learn the
Basics of solving a probability problem.
Coin experiment and learn the basics of
solving a probability problem.
Problems based on Probability (Basics)
Scan the QR Codes to watch our free videos
Points to Remember
Probability of an event always lies between 0 and 1.
[  0 = p ( x ) = 1 ]

p (happening an event) = 1 – p (Not happening that event)

?
?
?
p (sum of all possible outcomes) = 1
PROBABILITY 36
Happening of an Event provides with dierent Possible Outcomes. Here are the list of basic events and their outcomes which will help you to
start and understand the topic probability in a better manner.
```

Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

FAQs on Points to Remember: Probability - Mathematics (Maths) Class 10

 1. What is probability in Class 10 Maths?
Ans. Probability in Class 10 Maths refers to the measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 signifies no chance of occurrence and 1 signifies the event is certain to occur.
 2. How is probability calculated in Class 10 Maths?
Ans. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to find the probability of rolling a 6 on a fair die, the favorable outcome is 1 (rolling a 6) and the total possible outcomes are 6 (numbers 1 to 6 on the die). So, the probability would be 1/6.
 3. What are the different types of probability in Class 10 Maths?
Ans. There are three types of probability in Class 10 Maths: 1. Theoretical Probability: It is based on the assumption of an equally likely outcome. For example, the theoretical probability of rolling a 4 on a fair die is 1/6. 2. Experimental Probability: It is based on repeated experiments or trials. For example, if we roll a die 100 times and get a 4, 25 times, the experimental probability of rolling a 4 would be 25/100 or 1/4. 3. Subjective Probability: It is based on personal judgment or opinion. For example, if someone predicts the probability of rain tomorrow based on their gut feeling, it would be subjective probability.
 4. How is probability represented in Class 10 Maths?
Ans. Probability is represented as a fraction, decimal, or percentage in Class 10 Maths. It can be written in the form of P(A) = a/b, where P(A) represents the probability of event A, and a and b are integers.
 5. What are the applications of probability in real life?
Ans. Probability has various applications in real-life scenarios, including: 1. Weather Forecasting: Probability is used to predict the chances of rain, snow, or other weather conditions. 2. Gambling and Games: Probability helps in determining the odds and chances of winning in various games like card games, lotteries, and casinos. 3. Risk Assessment: Probability is used in assessing risks in insurance, finance, and investment decisions. 4. Sports: Probability is used to predict the outcome of sports events, such as the chances of a team winning a match. 5. Medical Research: Probability is used in clinical trials and medical research to determine the effectiveness of new treatments or drugs.

Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

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