INTRODUCTION, DEFINITION, EVENTS, SAMPLE SPACE.

1. PROBABILITY

2. INTRODUCTION TO PROBABILITY
• Probability is the branch of mathematics concerning numerical
descriptions of how likely an event is to occur, or how likely it is that a
proposition is true
• Most people use the terms such as chance, likelihood or uncertainties
about some events.

3. Applications of Probability
• Weather forecasting: Meteorologists use a specific tool and technique to
predict the weather forecast. They look at all the other historical database
of the days, which have similar characteristics of temperature, humidity,
and pressure, etc.
• Flipping a coin: There is no surety, either head will come or not. Both head
and tail have 1 out of 2, i.e., 50% chances to occur.
• Lottery Tickets: In a typical Lottery game, each player chooses six distinct
numbers from a particular range. If all the six numbers on a ticket match
with that of the winning lottery ticket, the ticket holder is a Jackpot winner-
regardless of the order of the numbers
• Playing Cards: There is a probability of getting a desired card when we
randomly pick one out of 52. For example, the probability of picking up an
ace in a 52 deck of cards is 4/52; since there are 4 aces in the deck.

4. Basic concepts of probability
• Probability always lie between zero and one, which reveals the
possibility that an event will occur.
• A probability of zero or close to zero implies that an event is very
improbable to occur and the probability of one or close to one gives
us high assurance of the event to occur.

5. • Experiment: Any process that results in two or more outcomes is
called an experiment.
• Example: Flipping a coin or drawing cards.
• Outcome: The result of a single trial of an experiment.
• Example: When we flip a coin, only two possibilities can occur, head
or tail. So the outcome of this experiment is a head or a tail.

6. • An event: A collection of one or more outcomes of an experiment to
which a probability is assigned.
• Sample space: All possible outcomes taken together represent the
“sample space” of an experiment.
• An event in probability is the subset of the respective sample space.

7. Example 1:
In rolling a six-sided die,
1. What is an experiment?
2. What is an outcome?
3. What is an event?
4. What is a sample space?
Solution:
Here, rolling a die is an experiment.
Numbers on the die such as 1,2,3,4,5 or 6 are the outcomes of this
experiment.
Specifying certain number from the die will be the event.
Sample space is the set of all outcome together, S= {1,2,3,4,5,6}

8. Example 2:
In tossing a coin twice,
1. What is an experiment?
2. What is an outcome?
3. What is an event?
4. What is a sample space?
Solution:
Here, tossing a coin twice is an experiment.
There are four possible outcomes. They are pairs of heads and tails. Thus HH, HT,
TH, TT are the outcomes.
Specifying a certain condition such as only heads appear on the coin is the event.
Sample space is the set of all outcome together, S= {HH, HT, TH, TT}