Courses

# Points to Remember: Probability Class 10 Notes | EduRev

## Class 10 : Points to Remember: Probability Class 10 Notes | EduRev

``` 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)

?
?
?
PLEASE KEEP IN MIND
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.
```
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

1 videos|13 docs

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;