Maths formulas # 04 :)
PROBABILITY
- Experiment:
An operation which can produce some
well-defined outcomes is called an experiment.
- 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:
- Rolling
an unbiased dice.
- Tossing
a fair coin.
- Drawing
a card from a pack of well-shuffled cards.
- Picking
up a ball of certain colour from a bag containing balls of different
colours.
Details:
- When
we throw a coin, then either a Head (H) or a Tail (T) appears.
- 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.
- 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.
- Sample
Space:
When we perform an experiment, then the
set S of all possible outcomes is called thesample space.
Examples:
- In tossing a
coin, S = {H, T}
- If two coins
are tossed, the S = {HH, HT, TH, TT}.
- In rolling a
dice, we have, S = {1, 2, 3, 4, 5, 6}.
4. 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.
P(E)
=
n(E)
.
n(S)
- Rolling an unbiased dice.
- Tossing a fair coin.
- Drawing a card from a pack of well-shuffled cards.
- Picking up a ball of certain colour from a bag containing balls of different colours.
- When we throw a coin, then either a Head (H) or a Tail (T) appears.
- 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.
- 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.
- In tossing a coin, S = {H, T}
- If two coins are tossed, the S = {HH, HT, TH, TT}.
- In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
n(E)
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n(S)
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