PROBABILITY

• Different types of events

All possible outcomes 1, 2, 3, 4, 5, 6

Rolling of a Die

All possible outcomes are present in an event, such an event is called SURE OR CERTAIN EVENT

Types of Events

1, 2, 3, 4, 5, 6

E is the event that a number less than 7 comes up

Favorable outcomes to E

P(E) =

= 1

Probability of Sure Or Certain Event = 1

All possible outcomes 1, 2, 3, 4, 5, 6

Only one outcome is present in an event such an event is called ELEMENTARY EVENT

F is the event of getting multiple of 4

Favourable outcomes to F

Rolling of a Die

P(F) =

Sum of Probabilities of all Elementary events of an experiment = 1

4

Types of Events

All possible outcomes 1, 2, 3, 4, 5, 6

Rolling of a Die

No outcome is favourable to an event such an event is called IMPOSSIBLE EVENT

G is the event of getting number greater than 8

No of Favourable outcomes to G

P(G) =

Probability of Impossible event = 0

= 0

Types of Events

All possible outcomes 1, 2, 3, 4, 5, 6

Rolling of a Die

1, 3, 5

X is the event of getting odd number

2, 4, 6

Y is the event of getting even number

Favourable outcomes to Y

Outcomes of X & Y are not same and together their outcomes gives all possible outcomes of the experiment

Hence, X & Y are said to be Complementary events

P(X) =

P(Y) =

P(X) + P (Y) =

= 1

i.e. P (X) + P (not X) = 1

Sum of Probabilities of Complementary events is equal to 1.

Favourable outcomes to X

What is favourable to X ?

Odd numbers are favourable

Types of Events

NOTE :

​

Probability of impossible event = 0

​

Probability of certain event = 1

​

Probability of any event lies between 0 and 1

​

Probability of any event cannot be negative

or it cannot be greater than 1