1. Experiment:
An operation
which can produce some well-defined outcomes is called an experiment.
2. Random
Experiment:
An experiment
in which all possible outcomes are know and the exact output cannot be
predicted in advance, is called a random experiment.
Examples:
i.
Rolling an unbiased dice.
ii.
Tossing a fair coin.
iii.
Drawing a card from a pack of well-shuffled cards.
iv.
Picking up a ball of certain colour from a bag containing balls of
different colours.
Details:
v.
When we throw a coin, then either a Head (H) or a Tail (T)
appears.
vi.
A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6
respectively. When we throw a die, the outcome is the number that appears on
its upper face.
vii.
A pack of cards has 52 cards.
It has 13 cards
of each suit, name Spades, Clubs, Hearts and Diamonds.
Cards of spades
and clubs are black cards.
Cards of hearts
and diamonds are red cards.
There are 4
honours of each unit.
There are Kings, Queens
and Jacks. These are all called face cards.
3. Sample Space:
When we perform
an experiment, then the set S of all possible outcomes is called the sample space.
Examples:
1. In tossing a
coin, S = {H, T}
2. If two coins
are tossed, the S = {HH, HT, TH, TT}.
3. In rolling a
dice, we have, S = {1, 2, 3, 4, 5, 6}.
Event:
Any subset of a
sample space is called an event.
Probability of Occurrence of an Event:
Let S be the
sample and let E be an event.
Then, E S.
Results on Probability:
.
P(S) = 1
i.
0 
P
(E) 1
ii.
P(
)
= 0
iii.
For any events A and B we have : P(A 
B)
= P(A) + P(B) - P(A 
B)
iv.
If A denotes (not-A), then P(A) = 1 - P(A).
Title :
Probability Synopsis
Description : 1. Experiment: An operation which can produce some well-defined outcomes is called an experiment. 2. Random Experiment:...
Rating :
5
